Evaluate (2!7!)/(4!8!)

$\frac{2! 7!}{4! 8!}$

Step 1

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

$\frac{2! 7!}{4! (8 \cdot 7!)}$

Step 2

Cancel the common factor of $7!$ .

Cancel the common factor.

$\frac{2! 7!}{4! (8 \cdot 7!)}$

Rewrite the expression.

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

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

Step 3

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

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

Step 4

Cancel the common factor of $2!$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{4 \cdot 3 \cdot 8}$

$\frac{1}{4 \cdot 3 \cdot 8}$

Step 5

Simplify the denominator.

Multiply $4$ by $3$ .

$\frac{1}{12 \cdot 8}$

Multiply $12$ by $8$ .

$\frac{1}{96}$

$\frac{1}{96}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{96}$

Decimal Form:

$0.01041\overline{6}$

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