Question

Ariel wants to choose 5 players for her basketball team. There are 7 players to choose from. How many different teams can aerial make?
A. 21
B. 35
C. 42
D. 56

Answer 1

The correct answer is:

A) 21

Explanation:

This is a combination of 7 objects taken 5 at a time:

$_nC_r=\frac{n!}{r!(n-r)!}$

In our case, n = 7 and r = 5:

$_7C_5=\frac{7!}{5!(7-5)!}=\frac{7!}{5!2!} \\ \\=\frac{7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1\times 2\times 1} \\ \\=\frac{5040}{240} = 21$