Finite Math Examples

9 P 3

${}_{9}P_{3}$

Step 1

Evaluate

9 P 3

${}_{9}P_{3}$ using the formula

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

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

\frac{9!}{(9 - 3)!}

$\frac{9!}{(9 - 3)!}$

Step 2

Subtract

3

$3$ from

9

$9$ .

\frac{9!}{(6)!}

$\frac{9!}{(6)!}$

Step 3

Simplify

\frac{9!}{(6)!}

$\frac{9!}{(6)!}$ .

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Step 3.1

Rewrite

9!

$9!$ as

9 \cdot 8 \cdot 7 \cdot 6!

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

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

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

Step 3.2

Cancel the common factor of

6!

$6!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide

$9 \cdot 8 \cdot 7$ by

$1$ .

$9 \cdot 8 \cdot 7$

$9 \cdot 8 \cdot 7$

Step 3.3

Multiply

$9 \cdot 8 \cdot 7$ .

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Step 3.3.1

Multiply

$9$ by

$8$ .

$72 \cdot 7$

Step 3.3.2

Multiply

$72$ by

$7$ .

$504$

$504$

$504$

${}_{9}P_{3}$

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