Finite Math Examples

${}_{6}P_{6}$

Step 1

Evaluate

${}_{6}P_{6}$ using the formula

${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{6!}{(6 - 6)!}$

Step 2

Subtract

$6$ from

$6$ .

$\frac{6!}{(0)!}$

Step 3

Simplify

$\frac{6!}{(0)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand

$6!$ to

$6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2

Multiply

$6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.1.2.1

Multiply

$6$ by

$5$ .

$\frac{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.2

Multiply

$30$ by

$4$ .

$\frac{120 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.3

Multiply

$120$ by

$3$ .

$\frac{360 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.4

Multiply

$360$ by

$2$ .

$\frac{720 \cdot 1}{(0)!}$

Step 3.1.2.5

Multiply

$720$ by

$1$ .

$\frac{720}{(0)!}$

$\frac{720}{(0)!}$

$\frac{720}{(0)!}$

Step 3.2

Expand

$(0)!$ to

$1$ .

$\frac{720}{1}$

Step 3.3

Divide

$720$ by

$1$ .

$720$

$720$

${}_{6}P_{6}$

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