In a university residence there are five single rooms five d

In a university residence there are five single rooms, five doubles, and five rooms which hold three students each. All rooms are numbered. In how many ways can 30 students be assigned to the 15 rooms?

Solution

There are 30P5 ways to choose those who go to the single rooms.

Now, there are 25C10 ways to choose 10 people who go to the doubles rooms. The 10 people can be permuted in 10!/(2!2!2!2!2!) = 113400 ways.

The other 15 people can be permuted in 15!/(3!3!3!3!3!) = 168168000 ways in the triples rooms.

Thus, there is a total of (30P5)*113400*168168000 = 3.26115*10^20 WAYS [ANSWER]