Finite Math Examples

${}_{15}C_{9}$

Step 1

Evaluate

${}_{15}C_{9}$ using the formula

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

$\frac{15!}{(15 - 9)! 9!}$

Step 2

Subtract

$9$ from

$15$ .

$\frac{15!}{(6)! 9!}$

Step 3

Simplify

$\frac{15!}{(6)! 9!}$ .

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Step 3.1

Rewrite

$15!$ as

$15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9!$ .

$\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9!}{(6)! 9!}$

Step 3.2

Cancel the common factor of

$9!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9!}{(6)! 9!}$

Step 3.2.2

Rewrite the expression.

$\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{(6)!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$15$ by

$14$ .

$\frac{210 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{(6)!}$

Step 3.3.2

Multiply

$210$ by

$13$ .

$\frac{2730 \cdot 12 \cdot 11 \cdot 10}{(6)!}$

Step 3.3.3

Multiply

$2730$ by

$12$ .

$\frac{32760 \cdot 11 \cdot 10}{(6)!}$

Step 3.3.4

Multiply

$32760$ by

$11$ .

$\frac{360360 \cdot 10}{(6)!}$

Step 3.3.5

Multiply

$360360$ by

$10$ .

$\frac{3603600}{(6)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(6)!$ to

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

$\frac{3603600}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

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

$5$ .

$\frac{3603600}{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$30$ by

$4$ .

$\frac{3603600}{120 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$120$ by

$3$ .

$\frac{3603600}{360 \cdot 2 \cdot 1}$

Step 3.4.2.4

Multiply

$360$ by

$2$ .

$\frac{3603600}{720 \cdot 1}$

Step 3.4.2.5

Multiply

$720$ by

$1$ .

$\frac{3603600}{720}$

Step 3.5

Divide

$3603600$ by

$720$ .

$5005$