If there are 6 letters and 6 corresponding en | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The number of ways to place $n$ letters in wrong envelopes is given by the derangement formula $D_n = n! \left[ 1 - \frac{1}{1!} + \frac{1}{2!} -

Vedclass · Accepted Answer

$265$

Vedclass · Answer

(A) The number of ways to place $n$ letters in wrong envelopes is given by the derangement formula $D_n = n! \left[ 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \dots + (-1)^n \frac{1}{n!} \right]$.For $n = 6$,the number of ways is $D_6 = 6! \left[ 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} + \frac{1}{6!} \right]$.$D_6 = 6! \left[ \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} + \frac{1}{6!} \right]$.$D_6 = \frac{720}{2} - \frac{720}{6} + \frac{720}{24} - \frac{720}{120} + \frac{720}{720}$.$D_6 = 360 - 120 + 30 - 6 + 1 = 265$.

If there are $6$ letters and $6$ corresponding envelopes,in how many ways can all the letters be placed in the wrong envelopes?

Similar Questions

The number of arrangements of all digits of $12345$ such that at least $3$ digits will not come in their original positions is

Choose the correct number of ways in which $15$ different books can be divided into $5$ heaps of equal number of books.

There are $4$ letters and $4$ envelopes. If the letters are placed into the envelopes at random,find the probability that all letters are placed in the wrong envelopes.

There are $7$ greeting cards, each of a different colour, and $7$ envelopes of the same $7$ colours as the cards. The number of ways in which the cards can be put in envelopes, so that exactly $4$ of the cards go into envelopes of the respective colour, is:

There are $4$ envelopes with addresses and $4$ corresponding letters. The probability that no letter goes into its correct envelope is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module