Question

There is a team of 31 people and two people are to be selected as co-captains. How many different ways can you select co-captains from the team?

Answer 1

ANSWER

465 different ways

STEP BY STEP EXPLANATION

Step 1: Using Combination

$C(n,r)\text{ = }\frac{n!}{r!(n-r)!}$

Step 2: from the question, n = 31 and r = 2

$\begin{gathered} C(31,\text{ 2) = }\frac{31!}{2!(31-2)!} \\ \text{ = }\frac{31\ast30\ast29!}{2!(29)!} \\ \text{ = }465 \end{gathered}$

Hence, you can select co-captains from the team in 465 different ways