Finite Math Examples

5 C 3

${}_{5}C_{3}$

Step 1

Evaluate

5 C 3

${}_{5}C_{3}$ using the formula

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

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

\frac{5!}{(5 - 3)! 3!}

$\frac{5!}{(5 - 3)! 3!}$

Step 2

Subtract

3

$3$ from

5

$5$ .

\frac{5!}{(2)! 3!}

$\frac{5!}{(2)! 3!}$

Step 3

Simplify

\frac{5!}{(2)! 3!}

$\frac{5!}{(2)! 3!}$ .

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Step 3.1

Rewrite

5!

$5!$ as

5 \cdot 4 \cdot 3!

$5 \cdot 4 \cdot 3!$ .

\frac{5 \cdot 4 \cdot 3!}{(2)! 3!}

$\frac{5 \cdot 4 \cdot 3!}{(2)! 3!}$

Step 3.2

Cancel the common factor of

3!

$3!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{5 \cdot 4 \cdot 3!}{(2)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{5 \cdot 4}{(2)!}$

$\frac{5 \cdot 4}{(2)!}$

Step 3.3

Multiply

$5$ by

$4$ .

$\frac{20}{(2)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(2)!$ to

$2 \cdot 1$ .

$\frac{20}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{20}{2}$

$\frac{20}{2}$

Step 3.5

Divide

$20$ by

$2$ .

$10$

$10$

${}_{5}C_{3}$

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