Question

Our basketball team has 10 players. we need to divide into two teams of 5 for an intra-squad scrimmage. in how many ways can we do this without restrictions?

Answer 1

There would be 252 different teams possible.

First, we need to find the total number of teams.
That would be: 10 x 9 x 8 x 7 x 6 = 30240

Then, divide that amount by the ways that you can mix up the 5 players on a team.  That is: 5 x 4 x 3 x 2 x 1 = 120

The final answer is: 30240 / 120 = 252