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 the same team?
Ok so we have 8 students and we want to make 2 teams.
Each team is 4 students.
Let Alice and Andrew be in the same team. Then, there are two more students needed in this team.
Now, we have 6 students and we want to choose 2, so: \(6C2\)
Now, there are 4 students remaining, and the other team is to be filled.
Thus, we want to choose 4 students from 4 students, This is done in one way only: \(4C4=1\)
Therefore, for both events to occur, we multiply: \(6C2*4C4=15*1=15\)
Thus, there are 15 ways.