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

 Mar 13, 2022
 #1
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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. 

 Mar 13, 2022
 #2
avatar+2437 
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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

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