Finite Math Examples

9 P 4

${}_{9}P_{4}$

Step 1

Evaluate

9 P 4

${}_{9}P_{4}$ using the formula

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

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

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

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

Step 2

Subtract

4

$4$ from

9

$9$ .

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

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

Step 3

Simplify

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

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

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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!}{(5)!}

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

Step 3.2

Cancel the common factor of

5!

$5!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

$9 \cdot 8 \cdot 7 \cdot 6$ by

$1$ .

$9 \cdot 8 \cdot 7 \cdot 6$

$9 \cdot 8 \cdot 7 \cdot 6$

Step 3.3

Multiply

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

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Step 3.3.1

Multiply

$9$ by

$8$ .

$72 \cdot 7 \cdot 6$

Step 3.3.2

Multiply

$72$ by

$7$ .

$504 \cdot 6$

Step 3.3.3

Multiply

$504$ by

$6$ .

$3024$

$3024$

$3024$

${}_{9}P_{4}$

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