Finite Math Examples

8 P 4

${}_{8}P_{4}$

Step 1

Evaluate

8 P 4

${}_{8}P_{4}$ using the formula

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

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

\frac{8!}{(8 - 4)!}

$\frac{8!}{(8 - 4)!}$

Step 2

Subtract

4

$4$ from

8

$8$ .

\frac{8!}{(4)!}

$\frac{8!}{(4)!}$

Step 3

Simplify

\frac{8!}{(4)!}

$\frac{8!}{(4)!}$ .

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Step 3.1

Rewrite

8!

$8!$ as

8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!

$8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!$ .

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

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

Step 3.2

Cancel the common factor of

4!

$4!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

$8 \cdot 7 \cdot 6 \cdot 5$ by

$1$ .

$8 \cdot 7 \cdot 6 \cdot 5$

$8 \cdot 7 \cdot 6 \cdot 5$

Step 3.3

Multiply

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

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Step 3.3.1

Multiply

$8$ by

$7$ .

$56 \cdot 6 \cdot 5$

Step 3.3.2

Multiply

$56$ by

$6$ .

$336 \cdot 5$

Step 3.3.3

Multiply

$336$ by

$5$ .

$1680$

$1680$

$1680$

${}_{8}P_{4}$

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