Finite Math Examples

13 C 2

${}_{13}C_{2}$

Step 1

Evaluate

13 C 2

${}_{13}C_{2}$ using the formula

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

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

\frac{13!}{(13 - 2)! 2!}

$\frac{13!}{(13 - 2)! 2!}$

Step 2

Subtract

2

$2$ from

13

$13$ .

\frac{13!}{(11)! 2!}

$\frac{13!}{(11)! 2!}$

Step 3

Simplify

\frac{13!}{(11)! 2!}

$\frac{13!}{(11)! 2!}$ .

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Step 3.1

Rewrite

13!

$13!$ as

13 \cdot 12 \cdot 11!

$13 \cdot 12 \cdot 11!$ .

\frac{13 \cdot 12 \cdot 11!}{(11)! 2!}

$\frac{13 \cdot 12 \cdot 11!}{(11)! 2!}$

Step 3.2

Cancel the common factor of

11!

$11!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{13 \cdot 12 \cdot 11!}{(11)! 2!}$

Step 3.2.2

Rewrite the expression.

$\frac{13 \cdot 12}{2!}$

$\frac{13 \cdot 12}{2!}$

Step 3.3

Multiply

$13$ by

$12$ .

$\frac{156}{2!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$2!$ to

$2 \cdot 1$ .

$\frac{156}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{156}{2}$

$\frac{156}{2}$

Step 3.5

Divide

$156$ by

$2$ .

$78$

$78$

${}_{13}C_{2}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$