Question

If 5 letters are taken out of 5 different envelopes. In how many ways, can they be reinserted in the envelopes so that no letter goes to its original envelopes?

• A. 9
• B. 44
• C. 120
• D. 24

Answer 1

The correct option is B 44

Number of possible de arrangement that are possible out of n letters in n envelopes.

The number of ways= $D_n=n!{\sum }_n^{k=0}\frac{(-1{)}^k}{k!}$

Number of possible de arrangements that are possible out of 5 letters in 5 envelopes
=$5!(1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!})$
=44