Posted by **vivian** on Monday, April 9, 2007 at 9:12pm.

There are 15 qualified applicants for 5 trainee positions in a fast-food program. How many groups of trainees can be selected?

I have a feeling that the answer is 75 but I'm not too sure. Any help is appreciated. Thank you!

The first trainee can be any one of 15 people, the second 14, and so on.

Assembling one group of five from 15 folks can be done 15!/10! ways.

Now if you are looking for how many groups can be formed from 15, then the answer is three groups, of five each.

The solution that Bob has given you is correct on the assumption that there are definite positions in the group of 5 people that are selected.

If there is no order in the group and we simply want to have groups of 5 trainees, then the solution would be 15(Choose)5 or

15!/(10!5!) = 3003

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