Finite Math Examples

${}_{18}P_{4}$

Step 1

Evaluate ${}_{18}P_{4}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{18!}{(18 - 4)!}$

Step 2

Subtract $4$ from $18$ .

$\frac{18!}{(14)!}$

Step 3

Simplify $\frac{18!}{(14)!}$ .

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Step 3.1

Rewrite $18!$ as $18 \cdot 17 \cdot 16 \cdot 15 \cdot 14!$ .

$\frac{18 \cdot 17 \cdot 16 \cdot 15 \cdot 14!}{(14)!}$

Step 3.2

Cancel the common factor of $14!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{18 \cdot 17 \cdot 16 \cdot 15 \cdot 14!}{(14)!}$

Step 3.2.2

Divide $18 \cdot 17 \cdot 16 \cdot 15$ by $1$ .

$18 \cdot 17 \cdot 16 \cdot 15$

Step 3.3

Multiply $18 \cdot 17 \cdot 16 \cdot 15$ .

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Step 3.3.1

Multiply $18$ by $17$ .

$306 \cdot 16 \cdot 15$

Step 3.3.2

Multiply $306$ by $16$ .

$4896 \cdot 15$

Step 3.3.3

Multiply $4896$ by $15$ .

$73440$