Question

What is the total number of ways in which Raj can distribute $9$ distinct gifts among his $8$ distinct girlfriends such that each of them gets at least one gift?

• A. $72\times 8!$
• B. $144\times 8!$
• C. $36\times 8!$
• D. $9!$

Answer 1

The correct option is A $72\times 8!$

Raj have $8$ distinct girlfriends

Number of distinct gifts Raj have $=9$

Select any $8$ gifts from the nine ${=}^9{C}_8=9$

Number of ways of distribution of $8$ gifts to his girlfriends$=8!$

Total number of ways Raj distributed gifts

$=9\times 8!\times 8=72\times 8!$