Finite Math Examples

${}_{99}P_{3}$

Step 1

Evaluate ${}_{99}P_{3}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{99!}{(99 - 3)!}$

Step 2

Subtract $3$ from $99$ .

$\frac{99!}{(96)!}$

Step 3

Simplify $\frac{99!}{(96)!}$ .

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Step 3.1

Rewrite $99!$ as $99 \cdot 98 \cdot 97 \cdot 96!$ .

$\frac{99 \cdot 98 \cdot 97 \cdot 96!}{(96)!}$

Step 3.2

Cancel the common factor of $96!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{99 \cdot 98 \cdot 97 \cdot 96!}{(96)!}$

Step 3.2.2

Divide $99 \cdot 98 \cdot 97$ by $1$ .

$99 \cdot 98 \cdot 97$

Step 3.3

Multiply $99 \cdot 98 \cdot 97$ .

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Step 3.3.1

Multiply $99$ by $98$ .

$9702 \cdot 97$

Step 3.3.2

Multiply $9702$ by $97$ .

$941094$