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

Solution (By Examveda Team)

One among 8 gfs will get 2 gifts and remaining 7 will get one. So total of 9 gifts will be distributed among 8 gfs. i.e; 11111112
Gf who will get 2 gifts can be find out in ⁸C₁ ways = 8 ways.
Now 2 gifts can be given to selected gf in ⁹C₂ ways. And remaining 7 gifts can be given to remaining 7 gf in 7! ways.
So total no of ways= 8 × ⁹C₂ × 7!
= $$\frac{{8 \times \left( {9 \times 8} \right)}}{{2 \times 7!}}$$
= 36 × 8 × 7!
= 36 × 8!