Find the Number of Possibilities seven permute seven

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

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

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

Subtract $7$ from $7$ .

$\frac{7!}{(0)!}$

Clarify $\frac{7!}{(0)!}$ .

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Clarify the numerator.

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Expand $7!$ to $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Simplify.

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First, multiply $7$ by $6$ .

$\frac{42 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Multiply $42$ by $5$ .

$\frac{210 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Initially, multiply $210$ by $4$ .

$\frac{840 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Multiply $840$ by $3$ .

$\frac{2520 \cdot 2 \cdot 1}{(0)!}$

Multiply $2520$ by $2$ .

$\frac{5040 \cdot 1}{(0)!}$

Multiply $5040$ by $1$ .

$\frac{5040}{(0)!}$

Expand $(0)!$ to $1$ .

$\frac{5040}{1}$

First, divide $5040$ by $1$ .

$5040$

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