Finite Math Examples

\frac{12!}{8! \cdot 4!}

$\frac{12!}{8! \cdot 4!}$

Step 1

Rewrite

12!

$12!$ as

12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!

$12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!$ .

\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{8! \cdot 4!}

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{8! \cdot 4!}$

Step 2

Cancel the common factor of

8!

$8!$ .

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Step 2.1

Cancel the common factor.

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{8! \cdot 4!}$

Step 2.2

Rewrite the expression.

$\frac{12 \cdot 11 \cdot 10 \cdot 9}{4!}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply

$12$ by

$11$ .

$\frac{132 \cdot 10 \cdot 9}{4!}$

Step 3.2

Multiply

$132$ by

$10$ .

$\frac{1320 \cdot 9}{4!}$

Step 3.3

Multiply

$1320$ by

$9$ .

$\frac{11880}{4!}$

Step 4

Simplify the denominator.

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Step 4.1

Expand

$4!$ to

$4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{11880}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 4.2

Multiply

$4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 4.2.1

Multiply

$4$ by

$3$ .

$\frac{11880}{12 \cdot 2 \cdot 1}$

Step 4.2.2

Multiply

$12$ by

$2$ .

$\frac{11880}{24 \cdot 1}$

Step 4.2.3

Multiply

$24$ by

$1$ .

$\frac{11880}{24}$

Step 5

Divide

$11880$ by

$24$ .

$495$

$\frac{12!}{8! \cdot 4!}$

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