Finite Math Examples

5 P 3

${}_{5}P_{3}$

Step 1

Evaluate

5 P 3

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

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

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

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

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

Step 2

Subtract

3

$3$ from

5

$5$ .

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

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

Step 3

Simplify

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

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

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Step 3.1

Rewrite

5!

$5!$ as

5 \cdot 4 \cdot 3 \cdot 2!

$5 \cdot 4 \cdot 3 \cdot 2!$ .

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

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

Step 3.2

Cancel the common factor of

2!

$2!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

$5 \cdot 4 \cdot 3$ by

$1$ .

$5 \cdot 4 \cdot 3$

$5 \cdot 4 \cdot 3$

Step 3.3

Multiply

$5 \cdot 4 \cdot 3$ .

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Step 3.3.1

Multiply

$5$ by

$4$ .

$20 \cdot 3$

Step 3.3.2

Multiply

$20$ by

$3$ .

$60$

$60$

$60$

${}_{5}P_{3}$

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