Evaluate (4!5!)/(2!7!)

$\frac{4! 5!}{2! 7!}$

Step 1

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

$\frac{4! 5!}{2! (7 \cdot 6 \cdot 5!)}$

Step 2

Cancel the common factor of $5!$ .

Cancel the common factor.

$\frac{4! 5!}{2! (7 \cdot 6 \cdot 5!)}$

Rewrite the expression.

$\frac{4!}{2! (7 \cdot 6)}$

Step 3

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

$\frac{4 \cdot 3 \cdot 2!}{2! (7 \cdot 6)}$

Step 4

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 \cdot 3 \cdot 2!$ .

$\frac{2 (2 \cdot 3 \cdot 2!)}{2! (7 \cdot 6)}$

Cancel the common factors.

Factor $2$ out of $2! (7 \cdot 6)$ .

$\frac{2 (2 \cdot 3 \cdot 2!)}{2 (2! (7 \cdot 3))}$

Cancel the common factor.

$\frac{2 (2 \cdot 3 \cdot 2!)}{2 (2! (7 \cdot 3))}$

Rewrite the expression.

$\frac{2 \cdot 3 \cdot 2!}{2! (7 \cdot 3)}$

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2 \cdot 3 \cdot 2!}{2! (7 \cdot 3)}$

Rewrite the expression.

$\frac{2 \cdot 2!}{2! \cdot (7)}$

Step 6

Cancel the common factor of $2!$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{7}$

Decimal Form:

$0.\overline{285714}$