Finite Math Examples

{}_{4}P_{3}

${}_{4}P_{3}$

Step 1

Evaluate

{}_{4}P_{3}

${}_{4}P_{3}$ using the formula

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

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

\frac{4!}{(4 - 3)!}

$\frac{4!}{(4 - 3)!}$

Step 2

Subtract

3

$3$ from

4

$4$ .

\frac{4!}{(1)!}

$\frac{4!}{(1)!}$

Step 3

Simplify

\frac{4!}{(1)!}

$\frac{4!}{(1)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand

4!

$4!$ to

4 \cdot 3 \cdot 2 \cdot 1

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

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

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

Step 3.1.2

Multiply

4 \cdot 3 \cdot 2 \cdot 1

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

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Step 3.1.2.1

Multiply

4

$4$ by

3

$3$ .

\frac{12 \cdot 2 \cdot 1}{(1)!}

$\frac{12 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.2

Multiply

12

$12$ by

2

$2$ .

\frac{24 \cdot 1}{(1)!}

$\frac{24 \cdot 1}{(1)!}$

Step 3.1.2.3

Multiply

24

$24$ by

1

$1$ .

\frac{24}{(1)!}

$\frac{24}{(1)!}$

\frac{24}{(1)!}

$\frac{24}{(1)!}$

\frac{24}{(1)!}

$\frac{24}{(1)!}$

Step 3.2

Expand

(1)!

$(1)!$ to

1

$1$ .

\frac{24}{1}

$\frac{24}{1}$

Step 3.3

Divide

24

$24$ by

1

$1$ .

24

$24$

24

$24$

{}_{4}P_{3}

${}_{4}P_{3}$

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

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