Finite Math Examples

${}_{9}P_{5}$

Step 1

Evaluate

${}_{9}P_{5}$ using the formula

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

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

Step 2

Subtract

$5$ from

$9$ .

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

Step 3

Simplify

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

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Step 3.1

Rewrite

$9!$ as

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!$ .

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{(4)!}$

Step 3.2

Cancel the common factor of

$4!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4!}{(4)!}$

Step 3.2.2

Divide

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5$ by

$1$ .

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5$

Step 3.3

Multiply

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5$ .

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Step 3.3.1

Multiply

$9$ by

$8$ .

$72 \cdot 7 \cdot 6 \cdot 5$

Step 3.3.2

Multiply

$72$ by

$7$ .

$504 \cdot 6 \cdot 5$

Step 3.3.3

Multiply

$504$ by

$6$ .

$3024 \cdot 5$

Step 3.3.4

Multiply

$3024$ by

$5$ .

$15120$

${}_{9}P_{5}$

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