Finite Math Examples

8 C 7

${}_{8}C_{7}$

Step 1

Evaluate

8 C 7

${}_{8}C_{7}$ using the formula

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

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

\frac{8!}{(8 - 7)! 7!}

$\frac{8!}{(8 - 7)! 7!}$

Step 2

Subtract

7

$7$ from

8

$8$ .

\frac{8!}{(1)! 7!}

$\frac{8!}{(1)! 7!}$

Step 3

Simplify

\frac{8!}{(1)! 7!}

$\frac{8!}{(1)! 7!}$ .

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Step 3.1

Rewrite

8!

$8!$ as

8 \cdot 7!

$8 \cdot 7!$ .

\frac{8 \cdot 7!}{(1)! 7!}

$\frac{8 \cdot 7!}{(1)! 7!}$

Step 3.2

Cancel the common factor of

7!

$7!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{8 \cdot 7!}{(1)! 7!}$

Step 3.2.2

Rewrite the expression.

$\frac{8}{(1)!}$

$\frac{8}{(1)!}$

Step 3.3

Expand

$(1)!$ to

$1$ .

$\frac{8}{1}$

Step 3.4

Divide

$8$ by

$1$ .

$8$

$8$

${}_{8}C_{7}$

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