Finite Math Examples

15 C 5

${}_{15}C_{5}$

Step 1

Evaluate

15 C 5

${}_{15}C_{5}$ using the formula

n C r = \frac{n!}{(n - r)! r!}

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

\frac{15!}{(15 - 5)! 5!}

$\frac{15!}{(15 - 5)! 5!}$

Step 2

Subtract

5

$5$ from

15

$15$ .

\frac{15!}{(10)! 5!}

$\frac{15!}{(10)! 5!}$

Step 3

Simplify

\frac{15!}{(10)! 5!}

$\frac{15!}{(10)! 5!}$ .

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Step 3.1

Rewrite

15!

$15!$ as

15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10!

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

\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10!}{(10)! 5!}

$\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10!}{(10)! 5!}$

Step 3.2

Cancel the common factor of

10!

$10!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10!}{(10)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{5!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$15$ by

$14$ .

$\frac{210 \cdot 13 \cdot 12 \cdot 11}{5!}$

Step 3.3.2

Multiply

$210$ by

$13$ .

$\frac{2730 \cdot 12 \cdot 11}{5!}$

Step 3.3.3

Multiply

$2730$ by

$12$ .

$\frac{32760 \cdot 11}{5!}$

Step 3.3.4

Multiply

$32760$ by

$11$ .

$\frac{360360}{5!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$5!$ to

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

$\frac{360360}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

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

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Step 3.4.2.1

Multiply

$5$ by

$4$ .

$\frac{360360}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$20$ by

$3$ .

$\frac{360360}{60 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$60$ by

$2$ .

$\frac{360360}{120 \cdot 1}$

Step 3.4.2.4

Multiply

$120$ by

$1$ .

$\frac{360360}{120}$

Step 3.5

Divide

$360360$ by

$120$ .

$3003$