Alice, Andrew, and six other students are to be divided into two teams of four people. How many ways are there to form the teams so that Alice and Andrew are on opposite teams?

Yoink Mar 2, 2019

#1**+2 **

We only need to consider one of the teams

On Alice's team .....we have 6 ways to choose the next person, 5 ways to choose the next one after that and 4 ways to choose the final person

So...we have ( 6 * 5 * 4) = 120 possible ways of choosing Alice's team

And the other players on each of Andrew's possible teams are the ones - by default - not chosen for Alice's team

So.....120 ways

CPhill Mar 2, 2019