Evaluate (9!)/(6!*3!)

$\frac{9!}{6! \cdot 3!}$

Step 1

Rewrite $9!$ as $9 \cdot 8 \cdot 7 \cdot 6!$ .

$\frac{9 \cdot 8 \cdot 7 \cdot 6!}{6! \cdot 3!}$

Step 2

Cancel the common factor of $6!$ .

Cancel the common factor.

$\frac{9 \cdot 8 \cdot 7 \cdot 6!}{6! \cdot 3!}$

Rewrite the expression.

$\frac{9 \cdot 8 \cdot 7}{3!}$

$\frac{9 \cdot 8 \cdot 7}{3!}$

Step 3

Simplify the numerator.

Multiply $9$ by $8$ .

$\frac{72 \cdot 7}{3!}$

Multiply $72$ by $7$ .

$\frac{504}{3!}$

$\frac{504}{3!}$

Step 4

Simplify the denominator.

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

$\frac{504}{3 \cdot 2 \cdot 1}$

Multiply $3 \cdot 2 \cdot 1$ .

Multiply $3$ by $2$ .

$\frac{504}{6 \cdot 1}$

Multiply $6$ by $1$ .

$\frac{504}{6}$

$\frac{504}{6}$

$\frac{504}{6}$

Step 5

Divide $504$ by $6$ .

$84$

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