Finite Math Examples

$\frac{20 P^{6}}{6!} - 20 C^{6}$

Step 1

Simplify the denominator.

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Step 1.1

Expand $6!$ to $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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

Step 1.2

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

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Step 1.2.1

Multiply $6$ by $5$ .

$\frac{20 P^{6}}{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1} - 20 C^{6}$

Step 1.2.2

Multiply $30$ by $4$ .

$\frac{20 P^{6}}{120 \cdot 3 \cdot 2 \cdot 1} - 20 C^{6}$

Step 1.2.3

Multiply $120$ by $3$ .

$\frac{20 P^{6}}{360 \cdot 2 \cdot 1} - 20 C^{6}$

Step 1.2.4

Multiply $360$ by $2$ .

$\frac{20 P^{6}}{720 \cdot 1} - 20 C^{6}$

Step 1.2.5

Multiply $720$ by $1$ .

$\frac{20 P^{6}}{720} - 20 C^{6}$

Step 2

Cancel the common factor of $20$ and $720$ .

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Step 2.1

Factor $20$ out of $20 P^{6}$ .

$\frac{20 (P^{6})}{720} - 20 C^{6}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $20$ out of $720$ .

$\frac{20 P^{6}}{20 \cdot 36} - 20 C^{6}$

Step 2.2.2

Cancel the common factor.

$\frac{20 P^{6}}{20 \cdot 36} - 20 C^{6}$

Step 2.2.3

Rewrite the expression.

$\frac{P^{6}}{36} - 20 C^{6}$