Question

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 be eight All Stars be seated in a row.

a. 242
b. 363
c. 432
d. 636

Answer 1

The total number of ways the eight All Stars can be seated in a row is 432 ways. (option c)

Step-by-step explanation:

To find the number of ways the eight All Stars can be seated in a row, we can consider the different groups they belong to.

There are three groups: Cubs, Red Sox, and Yankees. Since teammates insist on sitting together, each group should be considered as one unit.

So, we can treat the three groups as three units, and arrange them in a row.

The number of ways to arrange the units is 3! = 3 x 2 x 1 = 6.

Within each group, the teammates can be arranged in the group in 3! and 2! ways for the Cubs and Red Sox, respectively.

The Yankees have 2 players, so they can be arranged in 2! = 2 x 1 = 2 ways.

Therefore, the total number of ways the eight All Stars can be seated in a row is

6 x 3! x 3! x 2!

= 6 x 6 x 6 x 2

= 432 ways.