Finite Math Examples

11 C 3

${}_{11}C_{3}$

Step 1

Evaluate

11 C 3

${}_{11}C_{3}$ using the formula

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

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

\frac{11!}{(11 - 3)! 3!}

$\frac{11!}{(11 - 3)! 3!}$

Step 2

Subtract

3

$3$ from

11

$11$ .

\frac{11!}{(8)! 3!}

$\frac{11!}{(8)! 3!}$

Step 3

Simplify

\frac{11!}{(8)! 3!}

$\frac{11!}{(8)! 3!}$ .

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Step 3.1

Rewrite

11!

$11!$ as

11 \cdot 10 \cdot 9 \cdot 8!

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

\frac{11 \cdot 10 \cdot 9 \cdot 8!}{(8)! 3!}

$\frac{11 \cdot 10 \cdot 9 \cdot 8!}{(8)! 3!}$

Step 3.2

Cancel the common factor of

8!

$8!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{11 \cdot 10 \cdot 9 \cdot 8!}{(8)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{11 \cdot 10 \cdot 9}{3!}$

$\frac{11 \cdot 10 \cdot 9}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$11$ by

$10$ .

$\frac{110 \cdot 9}{3!}$

Step 3.3.2

Multiply

$110$ by

$9$ .

$\frac{990}{3!}$

$\frac{990}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{990}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{990}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{990}{6}$

$\frac{990}{6}$

$\frac{990}{6}$

Step 3.5

Divide

$990$ by

$6$ .

$165$

$165$

${}_{11}C_{3}$

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