Statistics Examples

${}_{9}P_{8}$

Step 1

Evaluate

${}_{9}P_{8}$ using the formula

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

$\frac{9!}{(9 - 8)!}$

Step 2

Subtract

$8$ from

$9$ .

$\frac{9!}{(1)!}$

Step 3

Simplify

$\frac{9!}{(1)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand

$9!$ to

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2

Multiply

$9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.1.2.1

Multiply

$9$ by

$8$ .

$\frac{72 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.2

Multiply

$72$ by

$7$ .

$\frac{504 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.3

Multiply

$504$ by

$6$ .

$\frac{3024 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.4

Multiply

$3024$ by

$5$ .

$\frac{15120 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.5

Multiply

$15120$ by

$4$ .

$\frac{60480 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.6

Multiply

$60480$ by

$3$ .

$\frac{181440 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.7

Multiply

$181440$ by

$2$ .

$\frac{362880 \cdot 1}{(1)!}$

Step 3.1.2.8

Multiply

$362880$ by

$1$ .

$\frac{362880}{(1)!}$

Step 3.2

Expand

$(1)!$ to

$1$ .

$\frac{362880}{1}$

Step 3.3

Divide

$362880$ by

$1$ .

$362880$

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