Evaluate (9!4!)/(7!2!)

$\frac{9! \cdot 4!}{7! \cdot 2!}$

Step 1

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

$\frac{9 \cdot 8 \cdot 7! \cdot 4!}{7! \cdot 2!}$

Step 2

Cancel the common factor of $7!$ .

Cancel the common factor.

$\frac{9 \cdot 8 \cdot 7! \cdot 4!}{7! \cdot 2!}$

Rewrite the expression.

$\frac{9 \cdot 8 \cdot 4!}{2!}$

$\frac{9 \cdot 8 \cdot 4!}{2!}$

Step 3

Rewrite $4!$ as $4 \cdot 3 \cdot 2!$ .

$\frac{9 \cdot 8 \cdot (4 \cdot 3 \cdot 2!)}{2!}$

Step 4

Cancel the common factor of $2!$ .

Cancel the common factor.

$\frac{9 \cdot 8 \cdot (4 \cdot 3 \cdot 2!)}{2!}$

Divide $9 \cdot 8 \cdot (4 \cdot 3)$ by $1$ .

$9 \cdot 8 \cdot (4 \cdot 3)$

$9 \cdot 8 \cdot (4 \cdot 3)$

Step 5

Multiply $9 \cdot 8 (4 \cdot 3)$ .

Multiply $9$ by $8$ .

$72 (4 \cdot 3)$

Multiply $4$ by $3$ .

$72 \cdot 12$

Multiply $72$ by $12$ .

$864$

$864$

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