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A company has 10 employees to choose from. They want 3 Representative. How many ways can temas be cosen if order foes not matter

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Answer to a math question A company has 10 employees to choose from. They want 3 Representative. How many ways can temas be cosen if order foes not matter

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Frederik
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103 Answers
\binom{n}{r} = \frac{n!}{r!(n-r)!}

Given:

\binom{10}{3} = \frac{10!}{3!(10-3)!} = \frac{10!}{3! \cdot 7!}

Simplify the factorials:

\frac{10!}{3! \cdot 7!} = \frac{10 \cdot 9 \cdot 8 \cdot 7!}{3! \cdot 7!}

Cancel \(7!\):

\frac{10 \cdot 9 \cdot 8}{3!} = \frac{10 \cdot 9 \cdot 8}{3 \cdot 2 \cdot 1}

Calculate the numerator and denominator:

\frac{720}{6} = 120

So, the number of ways to choose 3 representatives from 10 employees is:

\boxed{120}

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