Thread: Combinations/Permutations

From "Discrete Mathematics with Graph Theory"
by Goodaire and Parmenter

Page 236 # 16

There are 5 single rooms, 5 double rooms, and 5 triple rooms in a college. In how many ways can 30 students be assigned to the 15 rooms? (All rooms are numbered).

Thanks!

I'm thinking theres 15 spots (5 singles, 5 doubles, 5 triples) and 30 people go into those spots. But Then I'm confused from there.

There are 30 spots because 5 are singles(5), 5 are doubles (10), and 5 are triples (15).

Hello, ThatPinkSock!

There are 5 single rooms, 5 double rooms, and 5 triple rooms in a college.
In how many ways can 30 students be assigned to the 15 rooms? .(All rooms are numbered).

$\displaystyle \text{Answer: }\:\frac{30!}{(1!)^5(2!)^5(3!)^5}$