Question

You want to draft a four ­player tennis team. There are eight players to choose from. How many different teams can you form?

Answer 1

We want to make a 4 players team, and there are total 8 players. As we know the order of selection does not matter in a team of players, only the combination of players matters.

So we would use concept of Combinations and It will be choose 4 out of 8 players.

The formula for Combination is given as follows :-

$nCr = \frac{n!}{r!*(n-r)!} \\\\ Choose \;4 \;out \;of \;8 \;players \\\\ 8C4 = \frac{8!}{4!*(8-4)!} = \frac{8!}{4!*4!} \\\\ 8C4 = \frac{8*7*6*5*4*3*2*1}{(4*3*2*1)*(4*3*2*1)} = \frac{8*7*6*5}{4*3*2*1} =\frac{1,680}{24} = 70 \;combinations$

Hence, Total number of different teams = 70 combinations.