Finite Math Examples

5 C 1

${}_{5}C_{1}$

Step 1

Evaluate

5 C 1

${}_{5}C_{1}$ using the formula

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

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

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

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

Step 2

Subtract

1

$1$ from

5

$5$ .

\frac{5!}{(4)! 1!}

$\frac{5!}{(4)! 1!}$

Step 3

Simplify

\frac{5!}{(4)! 1!}

$\frac{5!}{(4)! 1!}$ .

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Step 3.1

Rewrite

5!

$5!$ as

5 \cdot 4!

$5 \cdot 4!$ .

\frac{5 \cdot 4!}{(4)! 1!}

$\frac{5 \cdot 4!}{(4)! 1!}$

Step 3.2

Cancel the common factor of

4!

$4!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{5 \cdot 4!}{(4)! 1!}$

Step 3.2.2

Rewrite the expression.

$\frac{5}{1!}$

$\frac{5}{1!}$

Step 3.3

Expand

$1!$ to

$1$ .

$\frac{5}{1}$

Step 3.4

Divide

$5$ by

$1$ .

$5$

$5$

${}_{5}C_{1}$

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