Find the Number of Possibilities 5 choose 2

${}_{5}C_{2}$

Evaluate ${}_{5}C_{2}$ using the formula ${}_{n}C_{r} = \frac{n!}{r! (n - r)!}$ .

$\frac{5!}{2! (5 - 2)!}$

Subtract $2$ from $5$ .

$\frac{5!}{2! (3)!}$

Simplify $\frac{5!}{2! (3)!}$ .

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Rewrite $5!$ as $5 \cdot 4 \cdot 3!$ .

$\frac{5 \cdot 4 \cdot 3!}{2! (3)!}$

Cancel the common factor of $3!$ .

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Cancel the common factor.

$\frac{5 \cdot 4 \cdot 3!}{2! (3)!}$

Rewrite the expression.

$\frac{5 \cdot 4}{2!}$

Multiply $5$ by $4$ .

$\frac{20}{2!}$

Simplify the denominator.

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Expand $2!$ to $2 \cdot 1$ .

$\frac{20}{2 \cdot 1}$

Multiply $2$ by $1$ .

$\frac{20}{2}$

Divide $20$ by $2$ .

$10$

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Find the Number of Possibilities 5 choose 2

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