Finite Math Examples

${}_{11}C_{2}$

Step 1

Evaluate

${}_{11}C_{2}$ using the formula

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

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

Step 2

Subtract

$2$ from

$11$ .

$\frac{11!}{(9)! 2!}$

Step 3

Simplify

$\frac{11!}{(9)! 2!}$ .

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Step 3.1

Rewrite

$11!$ as

$11 \cdot 10 \cdot 9!$ .

$\frac{11 \cdot 10 \cdot 9!}{(9)! 2!}$

Step 3.2

Cancel the common factor of

$9!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{11 \cdot 10 \cdot 9!}{(9)! 2!}$

Step 3.2.2

Rewrite the expression.

$\frac{11 \cdot 10}{2!}$

$\frac{11 \cdot 10}{2!}$

Step 3.3

Multiply

$11$ by

$10$ .

$\frac{110}{2!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$2!$ to

$2 \cdot 1$ .

$\frac{110}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{110}{2}$

$\frac{110}{2}$

Step 3.5

Divide

$110$ by

$2$ .

$55$

$55$

${}_{11}C_{2}$

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