Question

Ravish writes letters to his five friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?

• A. $109$
• B. $118$
• C. $119$
• D. None of these

Answer 1

The correct option is C

$119$

Explanation for the correct option:

We're told that a person writes letters to his five friends and addresses the envelopes accordingly.
We must evaluate the number of possible methods to position the letters in the envelopes so that at least two of them are in the incorrect envelopes.

The number of possible ways of putting $N$ letters into $N$ envelopes $=$ $N!$

Given $N=5$

The number of possible ways of putting $5$ letters into $5$ envelopes $=5!=120$

The number of ways of putting at least two envelopes in wrong envelopes $+$The number of possible ways of placing all $5$ letters in the correct boxes $=$$120$

The number of ways of placing all $5$ letters in the correct boxes $=$$1$

The number of ways of putting at least two envelopes in wrong envelopes $=$$120$$-1$

$=119$

Hence,option(C) is the correct answer.