Find the Number of Possibilities nine permute three

${}_{9}P_{3}$

Evaluate ${}_{9}P_{3}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{9!}{(9 - 3)!}$

Subtract $3$ from $9$ .

$\frac{9!}{(6)!}$

Clarify $\frac{9!}{(6)!}$ .

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Should be rewritten $9!$ as $9 \cdot 8 \cdot 7 \cdot 6!$ .

$\frac{9 \cdot 8 \cdot 7 \cdot 6!}{(6)!}$

The common factor should be canceled of $6!$ .

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Cancel the common factor.

$\frac{9 \cdot 8 \cdot 7 \cdot 6!}{(6)!}$

First, divide $9 \cdot 8 \cdot 7$ by $1$ .

$9 \cdot 8 \cdot 7$

First, multiply $9$ by $8$ .

$72 \cdot 7$

Multiply $72$ by $7$ .

$504$

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