Finite Math Examples

30 C 3

${}_{30}C_{3}$

Step 1

Evaluate

30 C 3

${}_{30}C_{3}$ using the formula

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

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

\frac{30!}{(30 - 3)! 3!}

$\frac{30!}{(30 - 3)! 3!}$

Step 2

Subtract

3

$3$ from

30

$30$ .

\frac{30!}{(27)! 3!}

$\frac{30!}{(27)! 3!}$

Step 3

Simplify

\frac{30!}{(27)! 3!}

$\frac{30!}{(27)! 3!}$ .

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Step 3.1

Rewrite

30!

$30!$ as

30 \cdot 29 \cdot 28 \cdot 27!

$30 \cdot 29 \cdot 28 \cdot 27!$ .

\frac{30 \cdot 29 \cdot 28 \cdot 27!}{(27)! 3!}

$\frac{30 \cdot 29 \cdot 28 \cdot 27!}{(27)! 3!}$

Step 3.2

Cancel the common factor of

27!

$27!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{30 \cdot 29 \cdot 28 \cdot 27!}{(27)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{30 \cdot 29 \cdot 28}{3!}$

$\frac{30 \cdot 29 \cdot 28}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$30$ by

$29$ .

$\frac{870 \cdot 28}{3!}$

Step 3.3.2

Multiply

$870$ by

$28$ .

$\frac{24360}{3!}$

$\frac{24360}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{24360}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{24360}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{24360}{6}$

$\frac{24360}{6}$

$\frac{24360}{6}$

Step 3.5

Divide

$24360$ by

$6$ .

$4060$

$4060$

${}_{30}C_{3}$

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