Finite Math Examples

6 C 5

${}_{6}C_{5}$

Step 1

Evaluate

6 C 5

${}_{6}C_{5}$ using the formula

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

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

\frac{6!}{(6 - 5)! 5!}

$\frac{6!}{(6 - 5)! 5!}$

Step 2

Subtract

5

$5$ from

6

$6$ .

\frac{6!}{(1)! 5!}

$\frac{6!}{(1)! 5!}$

Step 3

Simplify

\frac{6!}{(1)! 5!}

$\frac{6!}{(1)! 5!}$ .

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Step 3.1

Rewrite

6!

$6!$ as

6 \cdot 5!

$6 \cdot 5!$ .

\frac{6 \cdot 5!}{(1)! 5!}

$\frac{6 \cdot 5!}{(1)! 5!}$

Step 3.2

Cancel the common factor of

5!

$5!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{6 \cdot 5!}{(1)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{6}{(1)!}$

$\frac{6}{(1)!}$

Step 3.3

Expand

$(1)!$ to

$1$ .

$\frac{6}{1}$

Step 3.4

Divide

$6$ by

$1$ .

$6$

$6$

${}_{6}C_{5}$

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