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In a press conference before the All-Star Game, eight All-Stars will be taking questions. Three are Cubs, three are Red Sox, and two are Yankees. If teammates insist on sitting together, how many ways can the eight All-Stars be seated in a row?

Guest Apr 19, 2018
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I would guess that there would be 314 ways to arrange them.

I have seen this question a while back and that was what I calculated. Nobody answered back so i dont know if it was right.

 

somebody correct me if im wrong.

Donut  Apr 19, 2018
edited by Donut  Apr 19, 2018
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OK, I will try this: 

You can group the 8 into 3 different groups. And, as groups, you can seat them in:

3! = 6 ways. But the 3 Cubs can be seated in 3! ways, the 3 Red Sox can also be seated in 3! ways, and the 2 Yankees can be seated in 2! ways. So, altogether, they can be seated in:

3! x 3! x 3! x 2! = 432 ways. Somebody should check this.

Guest Apr 19, 2018

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