Finite Math Examples

$\frac{20 P^{14}}{14!} - 20 C^{14}$

Step 1

Simplify the denominator.

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Step 1.1

Expand $14!$ to $14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{20 P^{14}}{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2

Multiply $14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 1.2.1

Multiply $14$ by $13$ .

$\frac{20 P^{14}}{182 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.2

Multiply $182$ by $12$ .

$\frac{20 P^{14}}{2184 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.3

Multiply $2184$ by $11$ .

$\frac{20 P^{14}}{24024 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.4

Multiply $24024$ by $10$ .

$\frac{20 P^{14}}{240240 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.5

Multiply $240240$ by $9$ .

$\frac{20 P^{14}}{2162160 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.6

Multiply $2162160$ by $8$ .

$\frac{20 P^{14}}{17297280 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.7

Multiply $17297280$ by $7$ .

$\frac{20 P^{14}}{121080960 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.8

Multiply $121080960$ by $6$ .

$\frac{20 P^{14}}{726485760 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.9

Multiply $726485760$ by $5$ .

$\frac{20 P^{14}}{3632428800 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.10

Multiply $3632428800$ by $4$ .

$\frac{20 P^{14}}{14529715200 \cdot 3 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.11

Multiply $14529715200$ by $3$ .

$\frac{20 P^{14}}{43589145600 \cdot 2 \cdot 1} - 20 C^{14}$

Step 1.2.12

Multiply $43589145600$ by $2$ .

$\frac{20 P^{14}}{87178291200 \cdot 1} - 20 C^{14}$

Step 1.2.13

Multiply $87178291200$ by $1$ .

$\frac{20 P^{14}}{87178291200} - 20 C^{14}$

Step 2

Cancel the common factor of $20$ and $87178291200$ .

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Step 2.1

Factor $20$ out of $20 P^{14}$ .

$\frac{20 (P^{14})}{87178291200} - 20 C^{14}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $20$ out of $87178291200$ .

$\frac{20 P^{14}}{20 \cdot 4358914560} - 20 C^{14}$

Step 2.2.2

Cancel the common factor.

$\frac{20 P^{14}}{20 \cdot 4358914560} - 20 C^{14}$

Step 2.2.3

Rewrite the expression.

$\frac{P^{14}}{4358914560} - 20 C^{14}$