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?
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.