Evaluate (6!5!)/(8!2!)

$\frac{6! 5!}{8! 2!}$

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

$\frac{6! 5!}{8 \cdot 7 \cdot 6! 2!}$

Cancel the common factor of $6!$ .

Cancel the common factor.

$\frac{6! 5!}{8 \cdot 7 \cdot 6! 2!}$

Rewrite the expression.

$\frac{5!}{8 \cdot 72!}$

$\frac{5!}{8 \cdot 72!}$

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

$\frac{5 \cdot 4 \cdot 3 \cdot 2!}{8 \cdot 72!}$

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

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

$\frac{4 (5 \cdot 3 \cdot 2!)}{8 \cdot 72!}$

Cancel the common factors.

Factor $4$ out of $8 \cdot 72!$ .

$\frac{4 (5 \cdot 3 \cdot 2!)}{4 (2 \cdot 72!)}$

Cancel the common factor.

$\frac{4 (5 \cdot 3 \cdot 2!)}{4 (2 \cdot 72!)}$

Rewrite the expression.

$\frac{5 \cdot 3 \cdot 2!}{2 \cdot 72!}$

$\frac{5 \cdot 3 \cdot 2!}{2 \cdot 72!}$

$\frac{5 \cdot 3 \cdot 2!}{2 \cdot 72!}$

Cancel the common factor of $2!$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 \cdot 3}{2 \cdot 7}$

$\frac{5 \cdot 3}{2 \cdot 7}$

Multiply.

Multiply $5$ by $3$ .

$\frac{15}{2 \cdot 7}$

Multiply $2$ by $7$ .

$\frac{15}{14}$

$\frac{15}{14}$

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{14}$

Decimal Form:

$1.07142857 \dots$

Mixed Number Form:

$1 \frac{1}{14}$

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