Finite Math Examples

${}_{5}P_{4}$

Step 1

Evaluate

${}_{5}P_{4}$ using the formula

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

$\frac{5!}{(5 - 4)!}$

Step 2

Subtract

$4$ from

$5$ .

$\frac{5!}{(1)!}$

Step 3

Simplify

$\frac{5!}{(1)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand

$5!$ to

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

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

Step 3.1.2

Multiply

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

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Step 3.1.2.1

Multiply

$5$ by

$4$ .

$\frac{20 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.2

Multiply

$20$ by

$3$ .

$\frac{60 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.3

Multiply

$60$ by

$2$ .

$\frac{120 \cdot 1}{(1)!}$

Step 3.1.2.4

Multiply

$120$ by

$1$ .

$\frac{120}{(1)!}$

$\frac{120}{(1)!}$

$\frac{120}{(1)!}$

Step 3.2

Expand

$(1)!$ to

$1$ .

$\frac{120}{1}$

Step 3.3

Divide

$120$ by

$1$ .

$120$

$120$

${}_{5}P_{4}$

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