Finite Math 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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