Question

how many ways can a high school basketball coach find the 5 players for her starting lineup from 14 players?

Explanation:

Step1: Identify the combination formula

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 14\) (total number of players) and \(r=5\) (number of players to choose).

Step2: Calculate factorial values

\(n!=14! = 14\times13\times12\times11\times10\times9!\)
\(r!=5! = 5\times4\times3\times2\times1\)
\((n - r)!=(14 - 5)!=9!\)

Step3: Substitute into the formula

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Answer:

\(2002\)