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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?

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ANSWER

465 different ways

STEP BY STEP EXPLANATION

Step 1: Using Combination


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

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


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

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

User Pankaj Bisht
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