Find the Number of Possibilities seven permute five

${}_{7}P_{5}$

Evaluate ${}_{7}P_{5}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{7!}{(7 - 5)!}$

Subtract $5$ from $7$ .

$\frac{7!}{(2)!}$

Clarify $\frac{7!}{(2)!}$ .

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Should be rewritten $7!$ as $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

The common factor should be canceled of $2!$ .

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Cancel the common factor.

$\frac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}$

First, divide $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$ by $1$ .

$7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$

First, multiply $7$ by $6$ .

$42 \cdot 5 \cdot 4 \cdot 3$

Multiply $42$ by $5$ .

$210 \cdot 4 \cdot 3$

Initially, multiply $210$ by $4$ .

$840 \cdot 3$

Multiply $840$ by $3$ .

$2520$

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