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Bill is sent to a donut shop to purchase exactly six donuts. If the shop has four kinds of donuts and Bill is to get at least one of each kind, how many combinations will satisfy Bill's order requirements?

 

 I think the answer is 6, but I only have one try left before I get this problem wrong, please help! 

 Jun 14, 2019
 #1
avatar+8778 
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I think there are 10 different combinations that will satisfy Bill's order requirements.

 

Let's say the different kinds of donuts are  A, B, C,  and  D.

 

We know that Bill is always going to order A, B, C,  and  D, so that just leaves  2  unused orders ( 6 - 4 = 2 ).

 

To finish his orders, Bill can choose one of the following possibilities:

 

AA

AB

AC

AD

 

BB

BC

BD

 

CC

CD

 

DD

 

There are 10 different ways he can finish his orders, so that means there are 10 different combinations that will satisfy Bill's order requirements.

 Jun 14, 2019
 #2
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+1

hecticar got it right! Thank you!

Guest Jun 14, 2019

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