Finite Math Examples

8 C 4

${}_{8}C_{4}$

Step 1

Evaluate

8 C 4

${}_{8}C_{4}$ using the formula

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

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

\frac{8!}{(8 - 4)! 4!}

$\frac{8!}{(8 - 4)! 4!}$

Step 2

Subtract

4

$4$ from

8

$8$ .

\frac{8!}{(4)! 4!}

$\frac{8!}{(4)! 4!}$

Step 3

Simplify

\frac{8!}{(4)! 4!}

$\frac{8!}{(4)! 4!}$ .

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Step 3.1

Rewrite

8!

$8!$ as

8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!

$8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!$ .

\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{(4)! 4!}

$\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{(4)! 4!}$

Step 3.2

Cancel the common factor of

4!

$4!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{(4)! 4!}$

Step 3.2.2

Rewrite the expression.

$\frac{8 \cdot 7 \cdot 6 \cdot 5}{4!}$

$\frac{8 \cdot 7 \cdot 6 \cdot 5}{4!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$8$ by

$7$ .

$\frac{56 \cdot 6 \cdot 5}{4!}$

Step 3.3.2

Multiply

$56$ by

$6$ .

$\frac{336 \cdot 5}{4!}$

Step 3.3.3

Multiply

$336$ by

$5$ .

$\frac{1680}{4!}$

$\frac{1680}{4!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$4!$ to

$4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{1680}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$4$ by

$3$ .

$\frac{1680}{12 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$12$ by

$2$ .

$\frac{1680}{24 \cdot 1}$

Step 3.4.2.3

Multiply

$24$ by

$1$ .

$\frac{1680}{24}$

$\frac{1680}{24}$

$\frac{1680}{24}$

Step 3.5

Divide

$1680$ by

$24$ .

$70$

$70$

${}_{8}C_{4}$

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