Finite Math Examples

8 C 5

${}_{8}C_{5}$

Step 1

Evaluate

8 C 5

${}_{8}C_{5}$ using the formula

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

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

\frac{8!}{(8 - 5)! 5!}

$\frac{8!}{(8 - 5)! 5!}$

Step 2

Subtract

5

$5$ from

8

$8$ .

\frac{8!}{(3)! 5!}

$\frac{8!}{(3)! 5!}$

Step 3

Simplify

\frac{8!}{(3)! 5!}

$\frac{8!}{(3)! 5!}$ .

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Step 3.1

Rewrite

8!

$8!$ as

8 \cdot 7 \cdot 6 \cdot 5!

$8 \cdot 7 \cdot 6 \cdot 5!$ .

\frac{8 \cdot 7 \cdot 6 \cdot 5!}{(3)! 5!}

$\frac{8 \cdot 7 \cdot 6 \cdot 5!}{(3)! 5!}$

Step 3.2

Cancel the common factor of

5!

$5!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{8 \cdot 7 \cdot 6 \cdot 5!}{(3)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{8 \cdot 7 \cdot 6}{(3)!}$

$\frac{8 \cdot 7 \cdot 6}{(3)!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$8$ by

$7$ .

$\frac{56 \cdot 6}{(3)!}$

Step 3.3.2

Multiply

$56$ by

$6$ .

$\frac{336}{(3)!}$

$\frac{336}{(3)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(3)!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{336}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{336}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{336}{6}$

$\frac{336}{6}$

$\frac{336}{6}$

Step 3.5

Divide

$336$ by

$6$ .

$56$

$56$

${}_{8}C_{5}$

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