Finite Math Examples

${}_{7}P_{2}$

Step 1

Evaluate ${}_{7}P_{2}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

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

Step 2

Subtract $2$ from $7$ .

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

Step 3

Simplify $\frac{7!}{(5)!}$ .

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Step 3.1

Rewrite $7!$ as $7 \cdot 6 \cdot 5!$ .

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

Step 3.2

Cancel the common factor of $5!$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Divide $7 \cdot 6$ by $1$ .

$7 \cdot 6$

Step 3.3

Multiply $7$ by $6$ .

$42$

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