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Evaluate (15!)/((15-3)!(3!))

$\frac{15!}{(15 - 3)! (3!)}$

Step 1

Subtract $3$ from $15$ .

$\frac{15!}{(12)! 3!}$

Step 2

Rewrite $15!$ as $15 \cdot 14 \cdot 13 \cdot 12!$ .

$\frac{15 \cdot 14 \cdot 13 \cdot 12!}{(12)! 3!}$

Step 3

Cancel the common factor of $12!$ .

Cancel the common factor.

$\frac{15 \cdot 14 \cdot 13 \cdot 12!}{(12)! 3!}$

Rewrite the expression.

$\frac{15 \cdot 14 \cdot 13}{3!}$

$\frac{15 \cdot 14 \cdot 13}{3!}$

Step 4

Simplify the numerator.

Multiply $15$ by $14$ .

$\frac{210 \cdot 13}{3!}$

Multiply $210$ by $13$ .

$\frac{2730}{3!}$

$\frac{2730}{3!}$

Step 5

Simplify the denominator.

Expand $3!$ to $3 \cdot 2 \cdot 1$ .

$\frac{2730}{3 \cdot 2 \cdot 1}$

Multiply $3 \cdot 2 \cdot 1$ .

Multiply $3$ by $2$ .

$\frac{2730}{6 \cdot 1}$

Multiply $6$ by $1$ .

$\frac{2730}{6}$

$\frac{2730}{6}$

$\frac{2730}{6}$

Step 6

Divide $2730$ by $6$ .

$455$

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