Finite Math Examples

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

Step 1

Evaluate

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

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

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

Step 2

Subtract

$7$ from

$7$ .

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

Step 3

Simplify

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

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand

$7!$ to

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

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

Step 3.1.2

Multiply

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

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Step 3.1.2.1

Multiply

$7$ by

$6$ .

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

Step 3.1.2.2

Multiply

$42$ by

$5$ .

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

Step 3.1.2.3

Multiply

$210$ by

$4$ .

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

Step 3.1.2.4

Multiply

$840$ by

$3$ .

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

Step 3.1.2.5

Multiply

$2520$ by

$2$ .

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

Step 3.1.2.6

Multiply

$5040$ by

$1$ .

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

Step 3.2

Expand

$(0)!$ to

$1$ .

$\frac{5040}{1}$

Step 3.3

Divide

$5040$ by

$1$ .

$5040$

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

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