# Recent questions and answers in Combinatory

Ans is 16. Can anyone please explain how ? Can we use the pigeonhole principle to solve this problem?
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)
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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
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?
#Discrete-Mathematics: whether Binomial Theorem is part of the syllabus?
We select 38 even positive integers, all less than 1000. Prove that therewill be two of them whose difference is at most 26.
Why did use pigeonhole principle in bijective version, whereas in rossen it is not one-one?
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
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 $n$, $m$ 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) $1 - \frac{k!{n\choose k}}{m^k}$
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 ___________
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 ___________.
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?
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
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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 ?
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
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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?
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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?
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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
there are 5 pairs of different shoes.in how many ways can each person so that at least two person get a complete pair
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
How many ways are there to chose eight coins from piggy bank containing 100 identical pennies and 80 identical nickels.
The number of straight lines that can be drawn through 90 points.Given that 10 of them lie on a straight line.
A)1/16 B)1/15 C)1/4 D)NONE
Not able to solve this question. How to solve this type of questions?
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.
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?
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.
Why these 2 questions solved in different manner while it seems like both are same type questions?? Anyone Please.
Is there any difference between these 2 questions?? If yes then how can we solve this???
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
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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 ?
A, B, C, D, E, F are on circular table then, How many ways so that A and B sit always opposite?
Out of 10 couples, In how many ways we can select 2M and 2W and we should not select w1 and w9 simultaneously?
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