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Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.
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Recent questions and answers in Combinatory

Recent questions and answers in Combinatory

0 votes
1 answer 5 views
How many integers must you pick in order to be sure that at least two of them have same remainder when divided by 15____
Ans is 16. Can anyone please explain how ? Can we use the pigeonhole principle to solve this problem?
answered 1 day ago in Combinatory asqwer 633 points 5 views
0 votes
0 answers 7 views
How many ways 5 different ice creams can be distributed to three person without any restrictions
https://www.youtube.com/watch?v=xPm8ogLR_MU&list=PLbu_fGT0MPssMPJuhGZfYKn6MVqcDUjwJ&index=9 So, here I will assume that there are infinite no of ice cream of each type or One of each type . If former then , person 1 can receive one out of 5 ice creams then 2nd person can recieve ... implies ? Note: I am thinking from the shopkeeper side as if i am shopkeeper and i am distributing . (so not 3^5)
asked Jun 26 in Combinatory Saumyojit 5 points 7 views
1 vote
1 answer 131 views
Discrete Mathematics and its applications (Kenneth Rosen)
A multiple-choice test contains 10 questions. There are four possible answers for each question. In how many ways can a student answer the questions on the test if the student answers every question? In how many ways can a student answer the questions on the test ... there is no mention of it in question whether we should consider the order in which questions are solved or not? Thanks in advance
answered May 25 in Combinatory Deepakk Poonia (Dee) 1.7k points 131 views
0 votes
1 answer 29 views
A First Course in Probability by Sheldon Ross Chapter 1
In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together?
answered May 15 in Combinatory aryavart 73 points 29 views
0 votes
0 answers 19 views
Discrete Mathematical structures Chapter 5
#Discrete-Mathematics: whether Binomial Theorem is part of the syllabus?
#Discrete-Mathematics: whether Binomial Theorem is part of the syllabus?
asked May 10 in Combinatory Parag Tamhankar 5 points 19 views
0 votes
0 answers 13 views
discrete mathematics(topic) piegen hole
We select 38 even positive integers, all less than 1000. Prove that therewill be two of them whose difference is at most 26.
We select 38 even positive integers, all less than 1000. Prove that therewill be two of them whose difference is at most 26.
asked May 6 in Combinatory thispc295 5 points 13 views
0 votes
0 answers 20 views
Self doubt discrete mathematics counting
Why did use pigeonhole principle in bijective version, whereas in rossen it is not one-one?
Why did use pigeonhole principle in bijective version, whereas in rossen it is not one-one?
asked Apr 19 in Combinatory afroze 7 points 20 views
0 votes
1 answer 30 views
TIFR-GS2021 Question
A box contains 5 red marbles, 8 green marbles, 11 blue marbles, and 15 yellow marbles. We draw marbles uniformly at random without replacement from the box. What is the minimum number of marbles to be drawn to ensure that out of the marbles drawn, at least 7 are of the same colour? (A) 7 (B) 8 (C) 23 (D) 24 (E) 39
A box contains 5 red marbles, 8 green marbles, 11 blue marbles, and 15 yellow marbles. We draw marbles uniformly at random without replacement from the box. What is the minimum number of marbles to be drawn to ensure that out of the marbles drawn, at least 7 are of the same colour? (A) 7 (B) 8 (C) 23 (D) 24 (E) 39
answered Mar 24 in Combinatory zxy123 3.6k points 30 views
0 votes
0 answers 13 views
TIFR-GS2021 Question
Let $d$ be the number of positive square integers (that is, it is a square of some integer) that are factors of $20^5\times21^5$. Which of the following is true about $d$? (A) $50 \leq d < 100$ (B) $100 \leq d < 150$ (C) $150 \leq d < 200$ (D) $200 \leq d < 300$ (E) $300 \leq d$
Let $d$ be the number of positive square integers (that is, it is a square of some integer) that are factors of $20^5\times21^5$. Which of the following is true about $d$? (A) $50 \leq d < 100$ (B) $100 \leq d < 150$ (C) $150 \leq d < 200$ (D) $200 \leq d < 300$ (E) $300 \leq d$
asked Mar 24 in Combinatory zxy123 3.6k points 13 views
0 votes
0 answers 13 views
TIFR-GS2021 Question
Let $n$, $m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\{1, 2, , n\}$ of size $k$. Consider sampling a function uniformly at random from the set of all functions mapping $\{1, , n\}$ to $\{1, , m\}$. What is the probability ... $1 - \frac{k!{n\choose k}}{n^k}$ (E) $1 - \frac{k!{n\choose k}}{m^k}$
Let $n$, $m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\{1, 2, , n\}$ of size $k$. Consider sampling a function uniformly at random from the set of all functions mapping $\{1, , n\}$ to $\{1, , m\}$. What is the probability that $f$ is not ... $1 - \frac{k!{n\choose k}}{n^k}$ (E) $1 - \frac{k!{n\choose k}}{m^k}$
asked Mar 24 in Combinatory zxy123 3.6k points 13 views
4 votes
5 answers 1.2K views
GATE CSE 2021 Set 2 | Question: 50 | Video Solution
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
asked Feb 18 in Combinatory Arjun 1.5k points 1.2K views
5 votes
2 answers 1.1K views
GATE CSE 2021 Set 1 | Question: 19 | Video Solution
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
asked Feb 18 in Combinatory Arjun 1.5k points 1.1K views
0 votes
0 answers 28 views
NPTEL Assignment
In how many ways can one arrange five 1’s and five -1’s so that all ten partial sums (starting with the first summand) are nonnegative?
In how many ways can one arrange five 1’s and five -1’s so that all ten partial sums (starting with the first summand) are nonnegative?
asked Feb 6 in Combinatory Kindaichi 10 points 28 views
0 votes
0 answers 23 views
Kenneth H rosen Chapter 6 - "Counting" Section 6.4
Hi I have a doubt regarding a topic “Binomial coeffiecients and identities” so my doubt is, this topic is important for gate or not, means i study this section “Binomial coeffiecients and identities” of chapter 6 in Rosen book for gate or any questions will be asked from this section previously gate exams. Thank you
asked Jan 20 in Combinatory ykrishnay 103 points 23 views
1 vote
1 answer 38 views
Gate Applied Course Test Series
There are 20 intermediate stops on a route of a transport corporation bus. The number of ways in which the bus can stop at 6 of these intermediate stops such that no 2 stops are consecutive is ?
There are 20 intermediate stops on a route of a transport corporation bus. The number of ways in which the bus can stop at 6 of these intermediate stops such that no 2 stops are consecutive is ?
answered Jan 12 in Combinatory zxy123 3.6k points 38 views
0 votes
0 answers 16 views
#made-easy #discrete-maths
A group of 5 friends sitting on a bench. You have joined them with 8 sweets.All of you decided to share among ourself. The number of ways this distribution is possible is ___ i am getting ans 1287 but answer given is 20160 my approach is distribution of undistinguishable objects into distinguishable boxes. so formula is n+r-1Cr here n =6,r=8 so ans is 13C8
A group of 5 friends sitting on a bench. You have joined them with 8 sweets.All of you decided to share among ourself. The number of ways this distribution is possible is ___ i am getting ans 1287 but answer given is 20160 my approach is distribution of undistinguishable objects into distinguishable boxes. so formula is n+r-1Cr here n =6,r=8 so ans is 13C8
asked Dec 9, 2020 in Combinatory 404 found 37 points 16 views
1 vote
1 answer 63 views
Self Doubt. Combinatorics. How do I solve this question
There are 7 copies of the book, eight of a second book, and 9 of a third book. How many ways can two people divide them if each takes 12 books? How can I solve this easily?
answered Nov 11, 2020 in Combinatory SarathBaswa 855 points 63 views
1 vote
0 answers 19 views
Self Doubt in distribution problem
I have a small doubt which is :- Is identical to identical distribution the same as integer partition? Or in general, how to deal with distribution of identical letters to identical boxes?
I have a small doubt which is :- Is identical to identical distribution the same as integer partition? Or in general, how to deal with distribution of identical letters to identical boxes?
asked Nov 9, 2020 in Combinatory s_dr_13 15 points 19 views
1 vote
2 answers 123 views
Made easy - Discrete mathematics
How many ways can 10 balls be chosen from a container having 10 identical green balls , 5 identical yellow balls and 3 identical blue balls
How many ways can 10 balls be chosen from a container having 10 identical green balls , 5 identical yellow balls and 3 identical blue balls
answered Oct 30, 2020 in Combinatory ijnuhb 747 points 123 views
0 votes
0 answers 17 views
online search
there are 5 pairs of different shoes.in how many ways can each person so that at least two person get a complete pair
there are 5 pairs of different shoes.in how many ways can each person so that at least two person get a complete pair
asked Oct 20, 2020 in Combinatory ajay05908 5 points 17 views
0 votes
1 answer 36 views
Rosen - combinatorics ex 5.5 que 4
Every day a student randomly chooses a sandwich for lunch from a pile of wrapped sandwiches. If there are six kinds of sandwiches how many diff ways are there for the student to choose sandwiches for the 7 days of a week if the order in which sandwiches are chosen matters
Every day a student randomly chooses a sandwich for lunch from a pile of wrapped sandwiches. If there are six kinds of sandwiches how many diff ways are there for the student to choose sandwiches for the 7 days of a week if the order in which sandwiches are chosen matters
answered Oct 17, 2020 in Combinatory mayureshpatle 861 points 36 views
0 votes
2 answers 119 views
KENNETH ROSEN DISCRETE MATHEMATICS PAGE 432 Q11
How many ways are there to chose eight coins from piggy bank containing 100 identical pennies and 80 identical nickels.
How many ways are there to chose eight coins from piggy bank containing 100 identical pennies and 80 identical nickels.
answered Oct 9, 2020 in Combinatory Nikhil_dhama 225 points 119 views
0 votes
1 answer 52 views
Applied scholarship test
The number of straight lines that can be drawn through 90 points.Given that 10 of them lie on a straight line.
The number of straight lines that can be drawn through 90 points.Given that 10 of them lie on a straight line.
answered Sep 28, 2020 in Combinatory himanshu2021 139 points 52 views
0 votes
1 answer 32 views
Applied Scholarship Test
A)1/16 B)1/15 C)1/4 D)NONE
A)1/16 B)1/15 C)1/4 D)NONE
answered Sep 28, 2020 in Combinatory himanshu2021 139 points 32 views
0 votes
1 answer 49 views
Test Question of Applied Gate
Not able to solve this question. How to solve this type of questions?
Not able to solve this question. How to solve this type of questions?
answered Sep 16, 2020 in Combinatory Ehraz Hasan 366 points 49 views
0 votes
3 answers 147 views
Rosen-Chapter 8, Ex 8.5,Question 24
Find the probability that when a fair coin is flipped five times tails comes up exactly three times, the first and last flips come up tails, or the second and fourth flips come up heads.
Find the probability that when a fair coin is flipped five times tails comes up exactly three times, the first and last flips come up tails, or the second and fourth flips come up heads.
answered Sep 16, 2020 in Combinatory ijnuhb 747 points 147 views
0 votes
0 answers 53 views
Self doubt on Permutations and combination
If no three diagonals of a convex decagon meet at the same point inside the decagon, into how many line segments are the diagonals divided by their intersection?
If no three diagonals of a convex decagon meet at the same point inside the decagon, into how many line segments are the diagonals divided by their intersection?
asked Sep 9, 2020 in Combinatory ijnuhb 747 points 53 views
0 votes
0 answers 24 views
self doubt o this question
How can you get like for 2 I’s (3!*4)/2! ?? I know i am asking such a basic question but i’m little bit confused that’s why i asking.
How can you get like for 2 I’s (3!*4)/2! ?? I know i am asking such a basic question but i’m little bit confused that’s why i asking.
asked Sep 4, 2020 in Combinatory AbhayPrajapati 7 points 24 views
0 votes
0 answers 31 views
Self Doubt on Combinatorics
Why these 2 questions solved in different manner while it seems like both are same type questions?? Anyone Please.
Why these 2 questions solved in different manner while it seems like both are same type questions?? Anyone Please.
asked Sep 4, 2020 in Combinatory AbhayPrajapati 7 points 31 views
0 votes
1 answer 74 views
Self Doubt on Combinatorics
Is there any difference between these 2 questions?? If yes then how can we solve this???
Is there any difference between these 2 questions?? If yes then how can we solve this???
answered Sep 3, 2020 in Combinatory ijnuhb 747 points 74 views
0 votes
2 answers 89 views
Allan Career Institute: Discrete Math
Let $f\left ( x\right )$ be continuous probability density function of a random variable $X.$ Then probability of $a\leq X< b$ is $A)f\left ( b \right )-f\left ( a \right )$ $B)f\left ( a-b \right )$ $C)\int_{b}^{a}xf\left ( x \right )dx$ $D)\int_{b}^{a}f\left ( x \right )dx$ Plz give some link for probability of pdf
Let $f\left ( x\right )$ be continuous probability density function of a random variable $X.$ Then probability of $a\leq X< b$ is $A)f\left ( b \right )-f\left ( a \right )$ $B)f\left ( a-b \right )$ $C)\int_{b}^{a}xf\left ( x \right )dx$ $D)\int_{b}^{a}f\left ( x \right )dx$ Plz give some link for probability of pdf
answered Aug 16, 2020 in Combinatory jayeshasawa001 2.5k points 89 views
0 votes
1 answer 40 views
Self Doubt recurrence equation
answered Aug 16, 2020 in Combinatory Arkaprava 867 points 40 views
1 vote
1 answer 32 views
Kenneth Rosen(7th ed). Chapter 6. Example 16.
Each user on a computer system has a password, which is six to eight characters long, where each character is an uppercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there? Answer is given in book as : P^6 + P ... on for P^7 and P8. My question is why can't we calculate P^6 like 36^5 * C(6,1) * 10 ?
Each user on a computer system has a password, which is six to eight characters long, where each character is an uppercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there? Answer is given in book as : P^6 + P^7 + P^8; where P^6 = 36^6 – 26^6 and so on for P^7 and P8. My question is why can’t we calculate P^6 like 36^5 * C(6,1) * 10 ?
answered Aug 15, 2020 in Combinatory Arkaprava 867 points 32 views
0 votes
3 answers 64 views
Self Doubt. Combination, Circular. A, B, C, D, E, f are on circlular table.
A, B, C, D, E, F are on circular table then, How many ways so that A and B sit always opposite?
answered Aug 14, 2020 in Combinatory jayeshasawa001 2.5k points 64 views
0 votes
2 answers 74 views
Self-Doubt 10 couple, { 10 men and 10 women }, Number of Ways
Out of 10 couples, In how many ways we can select 2M and 2W and we should not select w1 and w9 simultaneously?
answered Aug 14, 2020 in Combinatory jayeshasawa001 2.5k points 74 views
1 vote
1 answer 36 views
K Rosen(7th ed). Chapter 6. Exercise 6.4. Q.17.
Question: Answer 1: Answer 2: I am not able to understand the solution.What’s happening here? Please help.
Question: Answer 1: Answer 2: I am not able to understand the solution.What’s happening here? Please help.
answered Aug 13, 2020 in Combinatory Arkaprava 867 points 36 views
1 vote
1 answer 90 views
nptel assignment
I am getting answer 64 didn’t know how answer is 40
I am getting answer 64 didn’t know how answer is 40
answered Aug 12, 2020 in Combinatory Arkaprava 867 points 90 views
0 votes
1 answer 21 views
#discrete mathematics #exponential generating function
Is exponential generating functions in gate syllabus?
answered Aug 12, 2020 in Combinatory Arkaprava 867 points 21 views
0 votes
1 answer 47 views
jee practice ques permutation
There are 5 apples 10 mangoes and 15 oranges in a basket. Then find number of ways of distributing 15 fruits each to 2 persons. a)56 b)64 c)66 d)72
There are 5 apples 10 mangoes and 15 oranges in a basket. Then find number of ways of distributing 15 fruits each to 2 persons. a)56 b)64 c)66 d)72
answered Aug 11, 2020 in Combinatory Arkaprava 867 points 47 views
0 votes
1 answer 44 views
Made easy topic wise tests
please explain this briefly!! .
please explain this briefly!! .
answered Aug 11, 2020 in Combinatory jayeshasawa001 2.5k points 44 views
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