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 Question from Aatir, a student: In how many ways can 12 members of volleyball team line up if the captain and assistant captain have to remain together.

Aatir,

We have two responses for you

First line up the 10 players who are not the captain or assistant captain. In how many ways can you do this? The captain and assistant captain can now be placed on the left end of the line, on the right end of the line or between any two players. That's 11 positions for the captain and assistant captain. If you put them in any one of the positions with the captain on the left of the assistant captain then you can create a different arrangement by placing the captain to the right of the assistant captain. How many arrangements is that is total?

Penny

Hi Aatir.

First ignore the captain and assistant captain. You have ten players and any order. Figure that out first.

Now consider that the pair must be somewhere in there, posted together. There are 11 possible positions, so multiply by 11.

Finally consider that the pair could be C-A or A-C (captain on left or captain on the right). That means doubling the possibilities, so multiply by 2.