Evaluate (4!8!)/(6!7!)

$\frac{4! 8!}{6! 7!}$

Step 1

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

$\frac{4! (8 \cdot 7!)}{6! 7!}$

Step 2

Cancel the common factor of $7!$ .

Cancel the common factor.

$\frac{4! (8 \cdot 7!)}{6! 7!}$

Rewrite the expression.

$\frac{4! \cdot (8)}{6!}$

$\frac{4! \cdot (8)}{6!}$

Step 3

Rewrite $6!$ as $6 \cdot 5 \cdot 4!$ .

$\frac{4! \cdot 8}{6 \cdot 5 \cdot 4!}$

Step 4

Cancel the common factor of $4!$ .

Cancel the common factor.

$\frac{4! \cdot 8}{6 \cdot 5 \cdot 4!}$

Rewrite the expression.

$\frac{8}{6 \cdot 5}$

$\frac{8}{6 \cdot 5}$

Step 5

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8$ .

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

Cancel the common factors.

Factor $2$ out of $6 \cdot 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{4}{3 \cdot 5}$

$\frac{4}{3 \cdot 5}$

$\frac{4}{3 \cdot 5}$

Step 6

Multiply $3$ by $5$ .

$\frac{4}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{15}$

Decimal Form:

$0.2\overline{6}$

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