Finite Math Examples

$\frac{{}_{5}P_{3}}{12 P^{4}}$

Step 1

Evaluate ${}_{5}P_{3}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{\frac{5!}{(5 - 3)!}}{12 P^{4}}$

Step 2

Subtract $3$ from $5$ .

$\frac{\frac{5!}{(2)!}}{12 P^{4}}$

Step 3

Simplify $\frac{5!}{(2)!}$ .

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Step 3.1

Rewrite $5!$ as $5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{\frac{5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}}{12 P^{4}}$

Step 3.2

Cancel the common factor of $2!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{\frac{5 \cdot 4 \cdot 3 \cdot 2!}{(2)!}}{12 P^{4}}$

Step 3.2.2

Divide $5 \cdot 4 \cdot 3$ by $1$ .

$\frac{5 \cdot 4 \cdot 3}{12 P^{4}}$

Step 3.3

Multiply $5 \cdot 4 \cdot 3$ .

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Step 3.3.1

Multiply $5$ by $4$ .

$\frac{20 \cdot 3}{12 P^{4}}$

Step 3.3.2

Multiply $20$ by $3$ .

$\frac{60}{12 P^{4}}$

Step 4

Cancel the common factor of $60$ and $12$ .

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Step 4.1

Factor $12$ out of $60$ .

$\frac{12 \cdot 5}{12 P^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $12$ out of $12 P^{4}$ .

$\frac{12 \cdot 5}{12 (P^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{12 \cdot 5}{12 P^{4}}$

Step 4.2.3

Rewrite the expression.

$\frac{5}{P^{4}}$