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?
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? Correct Answer 36 × 8!
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; 11111112Gf 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!