Finite Math Examples

13 C 5

${}_{13}C_{5}$

Step 1

Evaluate

13 C 5

${}_{13}C_{5}$ using the formula

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

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

\frac{13!}{(13 - 5)! 5!}

$\frac{13!}{(13 - 5)! 5!}$

Step 2

Subtract

5

$5$ from

13

$13$ .

\frac{13!}{(8)! 5!}

$\frac{13!}{(8)! 5!}$

Step 3

Simplify

\frac{13!}{(8)! 5!}

$\frac{13!}{(8)! 5!}$ .

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Step 3.1

Rewrite

13!

$13!$ as

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

$13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!$ .

\frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{(8)! 5!}

$\frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{(8)! 5!}$

Step 3.2

Cancel the common factor of

8!

$8!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{(8)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{5!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$13$ by

$12$ .

$\frac{156 \cdot 11 \cdot 10 \cdot 9}{5!}$

Step 3.3.2

Multiply

$156$ by

$11$ .

$\frac{1716 \cdot 10 \cdot 9}{5!}$

Step 3.3.3

Multiply

$1716$ by

$10$ .

$\frac{17160 \cdot 9}{5!}$

Step 3.3.4

Multiply

$17160$ by

$9$ .

$\frac{154440}{5!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$5!$ to

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

$\frac{154440}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

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

$4$ .

$\frac{154440}{20 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$20$ by

$3$ .

$\frac{154440}{60 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$60$ by

$2$ .

$\frac{154440}{120 \cdot 1}$

Step 3.4.2.4

Multiply

$120$ by

$1$ .

$\frac{154440}{120}$

Step 3.5

Divide

$154440$ by

$120$ .

$1287$