Finite Math Examples

${}_{12}C_{4}$

Step 1

Evaluate

${}_{12}C_{4}$ using the formula

${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{12!}{(12 - 4)! 4!}$

Step 2

Subtract

$4$ from

$12$ .

$\frac{12!}{(8)! 4!}$

Step 3

Simplify

$\frac{12!}{(8)! 4!}$ .

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Step 3.1

Rewrite

$12!$ as

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

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

Step 3.2

Cancel the common factor of

$8!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

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

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$12$ by

$11$ .

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

Step 3.3.2

Multiply

$132$ by

$10$ .

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

Step 3.3.3

Multiply

$1320$ by

$9$ .

$\frac{11880}{4!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$4!$ to

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

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

Step 3.4.2

Multiply

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

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Step 3.4.2.1

Multiply

$4$ by

$3$ .

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

Step 3.4.2.2

Multiply

$12$ by

$2$ .

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

Step 3.4.2.3

Multiply

$24$ by

$1$ .

$\frac{11880}{24}$

Step 3.5

Divide

$11880$ by

$24$ .

$495$

${}_{12}C_{4}$

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