Question

A football team consists of 20 offensive and 20 defensive players. The players are to be paired in groups of 2 for the purpose of determining roommates. If the pairing is done at random, (1) how many ways are there to divide the 40 players into unordered pairs of 2 each

Answer 1

780 ways

Explanation:

We have a football team consisting of 20 offensive and 20 defensive players.

The total number of the team would be:

20 + 20 = 40

Now, we must choose pairs, that is, 2, people, therefore it would be the combinations of 2 of 40 (40C2)

nCr = n! / (r! * (n-r)!)

replacing we have:

40C2 = 40! / (2! * (40-2)!) = 780

I mean there are a total of 780 ways