1
$\begingroup$

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 $756$).

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

1 Answer 1

1
$\begingroup$

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}$ = $(126)(6) = 756$

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .