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

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

Step 1

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

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

Step 2

Cancel the common factor of $5!$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Rewrite $5!$ as $5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{5 \cdot 4 \cdot 3 \cdot 2!}{2! (7 \cdot 6)}$

Step 4

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

Factor $2$ out of $5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{2 (5 \cdot 2 \cdot 3 \cdot 2!)}{2! (7 \cdot 6)}$

Cancel the common factors.

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

$\frac{2 (5 \cdot 2 \cdot 3 \cdot 2!)}{2 (2! (7 \cdot 3))}$

Cancel the common factor.

$\frac{2 (5 \cdot 2 \cdot 3 \cdot 2!)}{2 (2! (7 \cdot 3))}$

Rewrite the expression.

$\frac{5 \cdot 2 \cdot 3 \cdot 2!}{2! (7 \cdot 3)}$

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5 \cdot 2 \cdot 3 \cdot 2!}{2! (7 \cdot 3)}$

Rewrite the expression.

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

Step 6

Cancel the common factor of $2!$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 \cdot 2}{7}$

Step 7

Multiply $5$ by $2$ .

$\frac{10}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{7}$

Decimal Form:

$1.\overline{428571}$

Mixed Number Form:

$1 \frac{3}{7}$

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

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