Finite Math Examples

${}_{6}P_{3}$

Step 1

Evaluate ${}_{6}P_{3}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{6!}{(6 - 3)!}$

Step 2

Subtract $3$ from $6$ .

$\frac{6!}{(3)!}$

Step 3

Simplify $\frac{6!}{(3)!}$ .

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Step 3.1

Rewrite $6!$ as $6 \cdot 5 \cdot 4 \cdot 3!$ .

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

Step 3.2

Cancel the common factor of $3!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide $6 \cdot 5 \cdot 4$ by $1$ .

$6 \cdot 5 \cdot 4$

Step 3.3

Multiply $6 \cdot 5 \cdot 4$ .

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Step 3.3.1

Multiply $6$ by $5$ .

$30 \cdot 4$

Step 3.3.2

Multiply $30$ by $4$ .

$120$

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