Simple (probably) math question

General Questions
#1

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?

#2

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)
times
(8 x 7 x 6) / (2 x 3)

i.e. 1001 times 56

i.e. 56,056

#3

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.

http://www.cquest.utoronto.ca/geog/ggr270y/notes/not08a.html

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.