Finite Math Examples

$\frac{{}_{6}P_{2}}{5 P^{3}}$

Step 1

Evaluate ${}_{6}P_{2}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{\frac{6!}{(6 - 2)!}}{5 P^{3}}$

Step 2

Subtract $2$ from $6$ .

$\frac{\frac{6!}{(4)!}}{5 P^{3}}$

Step 3

Simplify $\frac{6!}{(4)!}$ .

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Step 3.1

Rewrite $6!$ as $6 \cdot 5 \cdot 4!$ .

$\frac{\frac{6 \cdot 5 \cdot 4!}{(4)!}}{5 P^{3}}$

Step 3.2

Cancel the common factor of $4!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{\frac{6 \cdot 5 \cdot 4!}{(4)!}}{5 P^{3}}$

Step 3.2.2

Divide $6 \cdot 5$ by $1$ .

$\frac{6 \cdot 5}{5 P^{3}}$

$\frac{6 \cdot 5}{5 P^{3}}$

Step 3.3

Multiply $6$ by $5$ .

$\frac{30}{5 P^{3}}$

$\frac{30}{5 P^{3}}$

Step 4

Cancel the common factor of $30$ and $5$ .

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Step 4.1

Factor $5$ out of $30$ .

$\frac{5 \cdot 6}{5 P^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $5 P^{3}$ .

$\frac{5 \cdot 6}{5 (P^{3})}$

Step 4.2.2

Cancel the common factor.

$\frac{5 \cdot 6}{5 P^{3}}$

Step 4.2.3

Rewrite the expression.

$\frac{6}{P^{3}}$

$\frac{6}{P^{3}}$

$\frac{6}{P^{3}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$