Awesome q2a theme
0 votes
31 views
an inefficient secretary places 5 different letters into 5 different addressed envelops at random.fnd the probability that at least one of the letters ill arrive at the proper destination.


the answer mentioned is 19/30
in Probability by (24 points) | 31 views

1 Answer

+2 votes

Study the concept of Derangements from a good resource. 

Derangement is basically the opposite of arrangement. In simple words, given $n$ objects and $n$ locations, how many ways can you arrange them such that all $n$ are in the wrong spots.

There is an accurate formula for this, but it can be approximated with $\frac{n!}{e}$

For $n = 5$, derangements $= \frac{5!}{e} \approx 44$

So there are $44$ ways to put all $5$ letters into the wrong envelopes, and $5!$ total ways of arranging the $5$ letters

$\therefore$ probability that all $5$ letters are in wrong envelopes $= \frac{44}{5!} = \frac{44}{120}$

$\therefore$ probability that at least one letter is in the right envelope $= 1 -\frac{44}{120} = \frac{76}{120} = \frac{19}{30} $

by (1.9k points)
0
thankyou for the response. a major doubt is cleared. :)
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users 2020 Aug 10 - 16
  1. Arkaprava

    404 Points

  2. jayeshasawa001

    198 Points

  3. SarathBaswa

    126 Points

  4. Ashutosh777

    67 Points

  5. toxicdesire

    20 Points

  6. Nilabja Sarkar

    12 Points

  7. premu

    10 Points

  8. iarnav

    7 Points

  9. Jhumpa_Sarma

    6 Points

  10. Patel0967

    6 Points

Weekly Top User (excluding moderators) will get free access to GATE Overflow Test Series for GATE 2021
Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.
Top Users Aug 2020
  1. Arkaprava

    404 Points

  2. jayeshasawa001

    203 Points

  3. Mellophi

    156 Points

  4. Ashutosh777

    143 Points

  5. SarathBaswa

    126 Points

  6. anurag sharma

    49 Points

  7. toxicdesire

    20 Points

  8. shashankrustagi2021

    16 Points

  9. premu

    16 Points

  10. Kushagra गुप्ता

    15 Points

7,769 questions
1,977 answers
11,275 comments
95,111 users