Finite Math Examples

9 C 5

${}_{9}C_{5}$

Step 1

Evaluate

9 C 5

${}_{9}C_{5}$ using the formula

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

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

\frac{9!}{(9 - 5)! 5!}

$\frac{9!}{(9 - 5)! 5!}$

Step 2

Subtract

5

$5$ from

9

$9$ .

\frac{9!}{(4)! 5!}

$\frac{9!}{(4)! 5!}$

Step 3

Simplify

\frac{9!}{(4)! 5!}

$\frac{9!}{(4)! 5!}$ .

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Step 3.1

Rewrite

9!

$9!$ as

9 \cdot 8 \cdot 7 \cdot 6 \cdot 5!

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5!$ .

\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5!}{(4)! 5!}

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5!}{(4)! 5!}$

Step 3.2

Cancel the common factor of

5!

$5!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5!}{(4)! 5!}$

Step 3.2.2

Rewrite the expression.

$\frac{9 \cdot 8 \cdot 7 \cdot 6}{(4)!}$

$\frac{9 \cdot 8 \cdot 7 \cdot 6}{(4)!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$9$ by

$8$ .

$\frac{72 \cdot 7 \cdot 6}{(4)!}$

Step 3.3.2

Multiply

$72$ by

$7$ .

$\frac{504 \cdot 6}{(4)!}$

Step 3.3.3

Multiply

$504$ by

$6$ .

$\frac{3024}{(4)!}$

$\frac{3024}{(4)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(4)!$ to

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

$\frac{3024}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

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

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Step 3.4.2.1

Multiply

$4$ by

$3$ .

$\frac{3024}{12 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$12$ by

$2$ .

$\frac{3024}{24 \cdot 1}$

Step 3.4.2.3

Multiply

$24$ by

$1$ .

$\frac{3024}{24}$

$\frac{3024}{24}$

$\frac{3024}{24}$

Step 3.5

Divide

$3024$ by

$24$ .

$126$

$126$

${}_{9}C_{5}$

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