Finite Math Examples

${}_{13}C_{3}$

Step 1

Evaluate

${}_{13}C_{3}$ using the formula

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

$\frac{13!}{(13 - 3)! 3!}$

Step 2

Subtract

$3$ from

$13$ .

$\frac{13!}{(10)! 3!}$

Step 3

Simplify

$\frac{13!}{(10)! 3!}$ .

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Step 3.1

Rewrite

$13!$ as

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

$\frac{13 \cdot 12 \cdot 11 \cdot 10!}{(10)! 3!}$

Step 3.2

Cancel the common factor of

$10!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{13 \cdot 12 \cdot 11 \cdot 10!}{(10)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{13 \cdot 12 \cdot 11}{3!}$

$\frac{13 \cdot 12 \cdot 11}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$13$ by

$12$ .

$\frac{156 \cdot 11}{3!}$

Step 3.3.2

Multiply

$156$ by

$11$ .

$\frac{1716}{3!}$

$\frac{1716}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{1716}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{1716}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{1716}{6}$

$\frac{1716}{6}$

$\frac{1716}{6}$

Step 3.5

Divide

$1716$ by

$6$ .

$286$

$286$

${}_{13}C_{3}$

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