Finite Math Examples

8 C 6

${}_{8}C_{6}$

Step 1

Evaluate

8 C 6

${}_{8}C_{6}$ using the formula

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

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

\frac{8!}{(8 - 6)! 6!}

$\frac{8!}{(8 - 6)! 6!}$

Step 2

Subtract

6

$6$ from

8

$8$ .

\frac{8!}{(2)! 6!}

$\frac{8!}{(2)! 6!}$

Step 3

Simplify

\frac{8!}{(2)! 6!}

$\frac{8!}{(2)! 6!}$ .

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Step 3.1

Rewrite

8!

$8!$ as

8 \cdot 7 \cdot 6!

$8 \cdot 7 \cdot 6!$ .

\frac{8 \cdot 7 \cdot 6!}{(2)! 6!}

$\frac{8 \cdot 7 \cdot 6!}{(2)! 6!}$

Step 3.2

Cancel the common factor of

6!

$6!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{8 \cdot 7 \cdot 6!}{(2)! 6!}$

Step 3.2.2

Rewrite the expression.

$\frac{8 \cdot 7}{(2)!}$

$\frac{8 \cdot 7}{(2)!}$

Step 3.3

Multiply

$8$ by

$7$ .

$\frac{56}{(2)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(2)!$ to

$2 \cdot 1$ .

$\frac{56}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{56}{2}$

$\frac{56}{2}$

Step 3.5

Divide

$56$ by

$2$ .

$28$

$28$

${}_{8}C_{6}$

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