Evaluate (8!)/(5!3!)

$\frac{8!}{5! 3!}$

Step 1

Rewrite $8!$ as $8 \cdot 7 \cdot 6 \cdot 5!$ .

$\frac{8 \cdot 7 \cdot 6 \cdot 5!}{5! 3!}$

Step 2

Cancel the common factor of $5!$ .

Cancel the common factor.

$\frac{8 \cdot 7 \cdot 6 \cdot 5!}{5! 3!}$

Rewrite the expression.

$\frac{8 \cdot 7 \cdot 6}{3!}$

$\frac{8 \cdot 7 \cdot 6}{3!}$

Step 3

Simplify the numerator.

Multiply $8$ by $7$ .

$\frac{56 \cdot 6}{3!}$

Multiply $56$ by $6$ .

$\frac{336}{3!}$

$\frac{336}{3!}$

Step 4

Simplify the denominator.

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

$\frac{336}{3 \cdot 2 \cdot 1}$

Multiply $3 \cdot 2 \cdot 1$ .

Multiply $3$ by $2$ .

$\frac{336}{6 \cdot 1}$

Multiply $6$ by $1$ .

$\frac{336}{6}$

$\frac{336}{6}$

$\frac{336}{6}$

Step 5

Divide $336$ by $6$ .

$56$

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