Evaluate (7!5!)/(9!3!)

$\frac{7! 5!}{9! 3!}$

Step 1

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

$\frac{7! 5!}{9 \cdot 8 \cdot 7! 3!}$

Step 2

Cancel the common factor of $7!$ .

Cancel the common factor.

$\frac{7! 5!}{9 \cdot 8 \cdot 7! 3!}$

Rewrite the expression.

$\frac{5!}{9 \cdot 83!}$

$\frac{5!}{9 \cdot 83!}$

Step 3

Rewrite $5!$ as $5 \cdot 4 \cdot 3!$ .

$\frac{5 \cdot 4 \cdot 3!}{9 \cdot 83!}$

Step 4

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $5 \cdot 4 \cdot 3!$ .

$\frac{4 (5 \cdot 3!)}{9 \cdot 83!}$

Cancel the common factors.

Factor $4$ out of $9 \cdot 83!$ .

$\frac{4 (5 \cdot 3!)}{4 (9 \cdot 23!)}$

Cancel the common factor.

$\frac{4 (5 \cdot 3!)}{4 (9 \cdot 23!)}$

Rewrite the expression.

$\frac{5 \cdot 3!}{9 \cdot 23!}$

$\frac{5 \cdot 3!}{9 \cdot 23!}$

$\frac{5 \cdot 3!}{9 \cdot 23!}$

Step 5

Cancel the common factor of $3!$ .

Cancel the common factor.

$\frac{5 \cdot 3!}{9 \cdot 2 3!}$

Rewrite the expression.

$\frac{5}{9 \cdot 2}$

$\frac{5}{9 \cdot 2}$

Step 6

Multiply $9$ by $2$ .

$\frac{5}{18}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{18}$

Decimal Form:

$0.2\overline{7}$

Related Questions