Eight single bedrooms in a dormitory are vacant. there would be 16 students to be admitted. how many ways can the students be admitted?

Question

anonymous · Answer

Do I get it right, 16 people to 8 beds?

jamesj · Answer

Sounds like college on good night.

valpey · Answer

If you are only picking 8 of the 16 it is 16!/8!

anonymous · Answer

nope

valpey · Answer

If you are picking all 16 at two to a room exactly it is 16!/(2^8) because within any one room order doesn't matter so you divide by two for each room.

anonymous · Answer

Is it not a combination? 
16!/(8!(16-8)!)

valpey · Answer

Not really. There are eight unique rooms so the 16 spots can be thought of a permutation. But within each room order doesn't matter.

valpey · Answer

A combination would be something like how many ways can I pick 8 students to go on a field trip out of a class of 16 where within any one possible set of 8 students I don't care about ordering them. That would be 16C8 or 16!/(8!(16-8)!).