Finite Math Examples

{}_{7}P_{7}

${}_{7}P_{7}$

Step 1

Evaluate

{}_{7}P_{7}

${}_{7}P_{7}$ using the formula

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

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

\frac{7!}{(7 - 7)!}

$\frac{7!}{(7 - 7)!}$

Step 2

Subtract

7

$7$ from

7

$7$ .

\frac{7!}{(0)!}

$\frac{7!}{(0)!}$

Step 3

Simplify

\frac{7!}{(0)!}

$\frac{7!}{(0)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand

7!

$7!$ to

7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1

$7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

\frac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}

$\frac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2

Multiply

7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1

$7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.1.2.1

Multiply

7

$7$ by

6

$6$ .

\frac{42 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}

$\frac{42 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.2

Multiply

42

$42$ by

5

$5$ .

\frac{210 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}

$\frac{210 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.3

Multiply

210

$210$ by

4

$4$ .

\frac{840 \cdot 3 \cdot 2 \cdot 1}{(0)!}

$\frac{840 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.4

Multiply

840

$840$ by

3

$3$ .

\frac{2520 \cdot 2 \cdot 1}{(0)!}

$\frac{2520 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.5

Multiply

2520

$2520$ by

2

$2$ .

\frac{5040 \cdot 1}{(0)!}

$\frac{5040 \cdot 1}{(0)!}$

Step 3.1.2.6

Multiply

5040

$5040$ by

1

$1$ .

\frac{5040}{(0)!}

$\frac{5040}{(0)!}$

\frac{5040}{(0)!}

$\frac{5040}{(0)!}$

\frac{5040}{(0)!}

$\frac{5040}{(0)!}$

Step 3.2

Expand

(0)!

$(0)!$ to

1

$1$ .

\frac{5040}{1}

$\frac{5040}{1}$

Step 3.3

Divide

5040

$5040$ by

1

$1$ .

5040

$5040$

5040

$5040$