# How many selections contain exactly $4$ green balls and $2$ yellow balls if you pick a subset of $6$ balls?

Question: Given a set of $$13$$ balls, $$9$$ of which are green and the other $$4$$ are yellow, if you pick a subset $$6$$ balls, how many selections contain exactly $$4$$ green balls and $$2$$ yellow balls?

I know that there are $$\binom{13}{6}$$ ways to pick a subset of 6 balls and that the number of ways to pick exactly $$4$$ green balls and $$2$$ yellow balls is equal to the number of ways to pick exactly 4 yellow balls out of 6 picks (since the other two will have to be yellow) and vice versa. Besides that, I have no idea how to solve this problem (though I'm pretty sure the answer is $$756$$).

• Just select $4$ green balls from the green pile, and $2$ yellow balls from the yellow pile. Nov 18, 2020 at 1:34
• Oh... of course. I'm an idiot. Nov 18, 2020 at 1:39

As Don Thousand said, all I needed to do was select $$4$$ green balls from the green pile and $$2$$ yellow balls from the yellow pile.
So $$\binom{9}{4}\binom{4}{2}$$ = $$(126)(6) = 756$$