Math Grouping Help: 20 Students, 4 Groups of 5, Different Schools

[ritwik06]

Homework Statement

Divide 20 students in 4 groups of 5 each. Find the number of ways of doing this?
Also find how can these gropus be sent to 4 different schools?

The Attempt at a Solution

I get both the answers as:
20C5*15C5*10C5*5C5

But my book gives two different answers for the above 2 different question. Help Please!

 

[CompuChip]

The first answer looks correct: you first pick 5 out of 20 for the first group, then 5 out of the remaining 15 for the second group, etc.

For the second question, I think you should forget about the students. You have 4 groups, and 4 schools to send them to. In abstract terms: you have 4 balls and 4 slots, how many possible ways are there to put each ball into one slot?