Find the Number of Possibilities 14 choose 2

${}_{14}C_{2}$

Evaluate ${}_{14}C_{2}$ using the formula ${}_{n}C_{r} = \frac{n!}{r! (n - r)!}$ .

$\frac{14!}{2! (14 - 2)!}$

Subtract $2$ from $14$ .

$\frac{14!}{2! (12)!}$

Simplify $\frac{14!}{2! (12)!}$ .

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Rewrite $14!$ as $14 \cdot 13 \cdot 12!$ .

$\frac{14 \cdot 13 \cdot 12!}{2! (12)!}$

Cancel the common factor of $12!$ .

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Cancel the common factor.

$\frac{14 \cdot 13 \cdot 12!}{2! (12)!}$

Rewrite the expression.

$\frac{14 \cdot 13}{2!}$

Multiply $14$ by $13$ .

$\frac{182}{2!}$

Simplify the denominator.

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

$\frac{182}{2 \cdot 1}$

Multiply $2$ by $1$ .

$\frac{182}{2}$

Divide $182$ by $2$ .

$91$

Find the Number of Possibilities 14 choose 2

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