Finite Math Examples

${}_{11}P_{4}$

Step 1

Evaluate ${}_{11}P_{4}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{11!}{(11 - 4)!}$

Step 2

Subtract $4$ from $11$ .

$\frac{11!}{(7)!}$

Step 3

Simplify $\frac{11!}{(7)!}$ .

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Step 3.1

Rewrite $11!$ as $11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!$ .

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!}{(7)!}$

Step 3.2

Cancel the common factor of $7!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7!}{(7)!}$

Step 3.2.2

Divide $11 \cdot 10 \cdot 9 \cdot 8$ by $1$ .

$11 \cdot 10 \cdot 9 \cdot 8$

Step 3.3

Multiply $11 \cdot 10 \cdot 9 \cdot 8$ .

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Step 3.3.1

Multiply $11$ by $10$ .

$110 \cdot 9 \cdot 8$

Step 3.3.2

Multiply $110$ by $9$ .

$990 \cdot 8$

Step 3.3.3

Multiply $990$ by $8$ .

$7920$