Question

The number of ways in which $5$ different books can be distributed among $10$ people if each person can get atmost one book is

• A. $252$
• B. ${10}^5$
• C. $5^{10}$
• D. ${}^{10}{C}_5.5!$

Answer 1

Answer: (D)

${}^{10}{C}_5.5!$

$5$ persons will receive the books and $5$ will not.

Hence no, of ways of choosing 5 persons from 10 people
$={}^{10}{C}_5$.

Now this can be internally permuted in $5!$ ways.

Hence total number of permutations will be

$={}^{10}{C}_5.5!$.