Simple (probably) math question

I’m sure there’s an easy way to do this, but I can’t seem to remember how. Maybe some math doper can help me out.

I have a class of 14 boys and 8 girls. We’re going on a field trip, and I want to put on one of the buses 10 boys and 5 girls (the rest of the kids ride on the other bus- doesn’t matter why). The order in which these 10 boys and 5 girls sit doesn’t matter, there just has to be 10 boys and 5 girls. I want to know how many possible different combinations of the 10 boys and 5 girls I could have on that bus. How do I figure this out?

You coulnt to number of different ways of choosing 10 out of 14, and the number of different ways of choosing 5 out of 8, the multiply them together:

(14 x 13 x 12 x 11) / (2 x 3 x 4)
(8 x 7 x 6) / (2 x 3)

i.e. 1001 times 56

i.e. 56,056

Giles is correct, and the following page (see Combinations Rule) explains the derivation of how many ways to select r items from a population of N. It gives you the general solution for this kind of problem. In case you actually wanted it.

And once you have the combinations of boys and combinations of girls, you simply multiply them to get all combinations of the combinations, as Giles states.