Finite Math Examples

12 C 2

${}_{12}C_{2}$

Step 1

Evaluate

12 C 2

${}_{12}C_{2}$ using the formula

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

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

\frac{12!}{(12 - 2)! 2!}

$\frac{12!}{(12 - 2)! 2!}$

Step 2

Subtract

2

$2$ from

12

$12$ .

\frac{12!}{(10)! 2!}

$\frac{12!}{(10)! 2!}$

Step 3

Simplify

\frac{12!}{(10)! 2!}

$\frac{12!}{(10)! 2!}$ .

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Step 3.1

Rewrite

12!

$12!$ as

12 \cdot 11 \cdot 10!

$12 \cdot 11 \cdot 10!$ .

\frac{12 \cdot 11 \cdot 10!}{(10)! 2!}

$\frac{12 \cdot 11 \cdot 10!}{(10)! 2!}$

Step 3.2

Cancel the common factor of

10!

$10!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{12 \cdot 11 \cdot 10!}{(10)! 2!}$

Step 3.2.2

Rewrite the expression.

$\frac{12 \cdot 11}{2!}$

$\frac{12 \cdot 11}{2!}$

Step 3.3

Multiply

$12$ by

$11$ .

$\frac{132}{2!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$2!$ to

$2 \cdot 1$ .

$\frac{132}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{132}{2}$

$\frac{132}{2}$

Step 3.5

Divide

$132$ by

$2$ .

$66$

$66$

${}_{12}C_{2}$

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