Finite Math Examples

${}_{5}P_{2}$

Step 1

Evaluate ${}_{5}P_{2}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{5!}{(5 - 2)!}$

Step 2

Subtract $2$ from $5$ .

$\frac{5!}{(3)!}$

Step 3

Simplify $\frac{5!}{(3)!}$ .

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Step 3.1

Rewrite $5!$ as $5 \cdot 4 \cdot 3!$ .

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

Step 3.2

Cancel the common factor of $3!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide $5 \cdot 4$ by $1$ .

$5 \cdot 4$

Step 3.3

Multiply $5$ by $4$ .

$20$

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