There are three rooms for #10# students, one with #3# beds, one with #2# beds and one with #5# beds. in how many ways can the #10# students be assigned to the three rooms so that each has a bed?

1 Answer
Jun 3, 2017

#2520#

Explanation:

If we counted each way the #10# students could be assigned to each of the #10# beds, then there would be #10!# ways.

However, note that we are not interested in which individual bed each student gets - only which room.

For each assignment of students to rooms, there are #3!*2!*5!# ways they can be assigned beds within those rooms.

Hence the number of different possible assignments to rooms is:

#(10!)/(3!2!5!) = 3628800/(6*2*120) = 2520#