Finite Math Examples

${}_{12}P_{12}$

Step 1

Evaluate ${}_{12}P_{12}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{12!}{(12 - 12)!}$

Step 2

Subtract $12$ from $12$ .

$\frac{12!}{(0)!}$

Step 3

Simplify $\frac{12!}{(0)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand $12!$ to $12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2

Multiply $12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.1.2.1

Multiply $12$ by $11$ .

$\frac{132 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.2

Multiply $132$ by $10$ .

$\frac{1320 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.3

Multiply $1320$ by $9$ .

$\frac{11880 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.4

Multiply $11880$ by $8$ .

$\frac{95040 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.5

Multiply $95040$ by $7$ .

$\frac{665280 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.6

Multiply $665280$ by $6$ .

$\frac{3991680 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.7

Multiply $3991680$ by $5$ .

$\frac{19958400 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.8

Multiply $19958400$ by $4$ .

$\frac{79833600 \cdot 3 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.9

Multiply $79833600$ by $3$ .

$\frac{239500800 \cdot 2 \cdot 1}{(0)!}$

Step 3.1.2.10

Multiply $239500800$ by $2$ .

$\frac{479001600 \cdot 1}{(0)!}$

Step 3.1.2.11

Multiply $479001600$ by $1$ .

$\frac{479001600}{(0)!}$

Step 3.2

Expand $(0)!$ to $1$ .

$\frac{479001600}{1}$

Step 3.3

Divide $479001600$ by $1$ .

$479001600$