With four yellow caps, and seven orange caps, how many ways can eleven boys be provided with caps?

Guest Mar 13, 2022

#1**0 **

I think this is a permutation problem.

If you order the Yellow and Orange caps in the following order:

Y, Y, Y, Y, O, O, O, O, O, O, O

It is different from:

Y, O, Y, O, Y, O, Y, O, O, O, O

So to me this is a permutation problem.

Apply formula.

11P11 = 39 916 800 ways

I'm not confident in my answer.

Guest Mar 13, 2022

#2**+2 **

I think it is \(11 \choose 7\). There are 7 ways to choose the boys with orange caps, and the rest have yellow caps.

Thus, there is \(\color{brown}\boxed{330}\) ways. (Note, \({11 \choose 7} = {11 \choose 4}\), so the answer would be the same either way.

BuilderBoi
Mar 13, 2022