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A store has four open checkout stands. Find the number of different ways that six customers can line up at these stands.

 

The way I did this (stars and bars):

Since there are 4 stands, I need to insert 3 dividers among these 6 people to make 4 groups.

Thus, I have 6+3=9 slots and 3 dividers to place.

 

9 choose 3 is 84.

 

Where am I wrong?

 

Other answers I have tried: 21 (84/4), 120 (10 choose 3), 165 (11 choose 3), 35 (7 choose 3)

 Mar 15, 2020
 #1
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Me again, I closed the window so I can't edit.

Using a Java program, I bashed it and found 56. That, too, is wrong.

Confusion?

 Mar 15, 2020
 #2
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I got it. It is 84, but you have to multiply by 6!=720 (the number of ways to arrange the six people).

Thus you get 84*720=60480.

 Mar 15, 2020

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