Finite Math Examples

$\frac{14!}{2! (14! - 2!)}$

Step 1

Rewrite $14!$ as $14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{2! (14! - 2!)}$

Step 2

Cancel the common factor of $2!$ .

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Step 2.1

Cancel the common factor.

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{2! (14! - 2!)}$

Step 2.2

Rewrite the expression.

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $14$ by $13$ .

$\frac{182 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.2

Multiply $182$ by $12$ .

$\frac{2184 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.3

Multiply $2184$ by $11$ .

$\frac{24024 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.4

Multiply $24024$ by $10$ .

$\frac{240240 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.5

Multiply $240240$ by $9$ .

$\frac{2162160 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.6

Multiply $2162160$ by $8$ .

$\frac{17297280 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.7

Multiply $17297280$ by $7$ .

$\frac{121080960 \cdot 6 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.8

Multiply $121080960$ by $6$ .

$\frac{726485760 \cdot 5 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.9

Multiply $726485760$ by $5$ .

$\frac{3632428800 \cdot 4 \cdot 3}{14! - 2!}$

Step 3.10

Multiply $3632428800$ by $4$ .

$\frac{14529715200 \cdot 3}{14! - 2!}$

Step 3.11

Multiply $14529715200$ by $3$ .

$\frac{43589145600}{14! - 2!}$

Step 4

Simplify the denominator.

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Step 4.1

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

$\frac{43589145600}{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2

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 4.2.1

Multiply $14$ by $13$ .

$\frac{43589145600}{182 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.2

Multiply $182$ by $12$ .

$\frac{43589145600}{2184 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.3

Multiply $2184$ by $11$ .

$\frac{43589145600}{24024 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.4

Multiply $24024$ by $10$ .

$\frac{43589145600}{240240 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.5

Multiply $240240$ by $9$ .

$\frac{43589145600}{2162160 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.6

Multiply $2162160$ by $8$ .

$\frac{43589145600}{17297280 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.7

Multiply $17297280$ by $7$ .

$\frac{43589145600}{121080960 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.8

Multiply $121080960$ by $6$ .

$\frac{43589145600}{726485760 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.9

Multiply $726485760$ by $5$ .

$\frac{43589145600}{3632428800 \cdot 4 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.10

Multiply $3632428800$ by $4$ .

$\frac{43589145600}{14529715200 \cdot 3 \cdot 2 \cdot 1 - 2!}$

Step 4.2.11

Multiply $14529715200$ by $3$ .

$\frac{43589145600}{43589145600 \cdot 2 \cdot 1 - 2!}$

Step 4.2.12

Multiply $43589145600$ by $2$ .

$\frac{43589145600}{87178291200 \cdot 1 - 2!}$

Step 4.2.13

Multiply $87178291200$ by $1$ .

$\frac{43589145600}{87178291200 - 2!}$

Step 4.3

Expand $2!$ to $2 \cdot 1$ .

$\frac{43589145600}{87178291200 - (2 \cdot 1)}$

Step 4.4

Multiply $2$ by $1$ .

$\frac{43589145600}{87178291200 - 1 \cdot 2}$

Step 4.5

Multiply $- 1$ by $2$ .

$\frac{43589145600}{87178291200 - 2}$

Step 4.6

Subtract $2$ from $87178291200$ .

$\frac{43589145600}{87178291198}$

Step 5

Cancel the common factor of $43589145600$ and $87178291198$ .

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Step 5.1

Factor $2$ out of $43589145600$ .

$\frac{2 (21794572800)}{87178291198}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $87178291198$ .

$\frac{2 \cdot 21794572800}{2 \cdot 43589145599}$

Step 5.2.2

Cancel the common factor.

$\frac{2 \cdot 21794572800}{2 \cdot 43589145599}$

Step 5.2.3

Rewrite the expression.

$\frac{21794572800}{43589145599}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{21794572800}{43589145599}$

Decimal Form:

$0.50000000 \dots$