Finite Math Examples

${}_{12}C_{6}$

Step 1

Evaluate

${}_{12}C_{6}$ using the formula

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

$\frac{12!}{(12 - 6)! 6!}$

Step 2

Subtract

$6$ from

$12$ .

$\frac{12!}{(6)! 6!}$

Step 3

Simplify

$\frac{12!}{(6)! 6!}$ .

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Step 3.1

Rewrite

$12!$ as

$12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!$ .

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{(6)! 6!}$

Step 3.2

Cancel the common factor of

$6!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{(6)! 6!}$

Step 3.2.2

Rewrite the expression.

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{6!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$12$ by

$11$ .

$\frac{132 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{6!}$

Step 3.3.2

Multiply

$132$ by

$10$ .

$\frac{1320 \cdot 9 \cdot 8 \cdot 7}{6!}$

Step 3.3.3

Multiply

$1320$ by

$9$ .

$\frac{11880 \cdot 8 \cdot 7}{6!}$

Step 3.3.4

Multiply

$11880$ by

$8$ .

$\frac{95040 \cdot 7}{6!}$

Step 3.3.5

Multiply

$95040$ by

$7$ .

$\frac{665280}{6!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$6!$ to

$6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{665280}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$6$ by

$5$ .

$\frac{665280}{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$30$ by

$4$ .

$\frac{665280}{120 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$120$ by

$3$ .

$\frac{665280}{360 \cdot 2 \cdot 1}$

Step 3.4.2.4

Multiply

$360$ by

$2$ .

$\frac{665280}{720 \cdot 1}$

Step 3.4.2.5

Multiply

$720$ by

$1$ .

$\frac{665280}{720}$

Step 3.5

Divide

$665280$ by

$720$ .

$924$