Finite Math Examples

$\frac{11!}{11! \cdot 8!}$

Step 1

Cancel the common factor of $11!$ .

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Step 1.1

Cancel the common factor.

$\frac{11!}{11! \cdot 8!}$

Step 1.2

Rewrite the expression.

$\frac{1}{8!}$

Step 2

Simplify the denominator.

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Step 2.1

Expand $8!$ to $8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{1}{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 2.2

Multiply $8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.2.1

Multiply $8$ by $7$ .

$\frac{1}{56 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 2.2.2

Multiply $56$ by $6$ .

$\frac{1}{336 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 2.2.3

Multiply $336$ by $5$ .

$\frac{1}{1680 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 2.2.4

Multiply $1680$ by $4$ .

$\frac{1}{6720 \cdot 3 \cdot 2 \cdot 1}$

Step 2.2.5

Multiply $6720$ by $3$ .

$\frac{1}{20160 \cdot 2 \cdot 1}$

Step 2.2.6

Multiply $20160$ by $2$ .

$\frac{1}{40320 \cdot 1}$

Step 2.2.7

Multiply $40320$ by $1$ .

$\frac{1}{40320}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{40320}$

Decimal Form:

$2.48015873 \cdot 10^{- 5}$