Finite Math Examples

$\frac{\frac{26!}{3! \cdot 23!}}{\frac{48!}{3! \cdot 45!}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{26!}{3! \cdot 23!} \cdot \frac{3! \cdot 45!}{48!}$

Step 2

Cancel the common factor of $3!$ .

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Step 2.1

Factor $3!$ out of $3! \cdot 23!$ .

$\frac{26!}{3! (23!)} \cdot \frac{3! \cdot 45!}{48!}$

Step 2.2

Factor $3!$ out of $3! \cdot 45!$ .

$\frac{26!}{3! (23!)} \cdot \frac{3! (45!)}{48!}$

Step 2.3

Cancel the common factor.

$\frac{26!}{3! 23!} \cdot \frac{3! 45!}{48!}$

Step 2.4

Rewrite the expression.

$\frac{26!}{23!} \cdot \frac{45!}{48!}$

Step 3

Multiply $\frac{26!}{23!}$ by $\frac{45!}{48!}$ .

$\frac{26! 45!}{23! 48!}$

Step 4

Rewrite $48!$ as $48 \cdot 47 \cdot 46 \cdot 45!$ .

$\frac{26! 45!}{23! (48 \cdot 47 \cdot 46 \cdot 45!)}$

Step 5

Cancel the common factor of $45!$ .

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Step 5.1

Cancel the common factor.

$\frac{26! 45!}{23! (48 \cdot 47 \cdot 46 \cdot 45!)}$

Step 5.2

Rewrite the expression.

$\frac{26!}{23! (48 \cdot 47 \cdot 46)}$

Step 6

Rewrite $26!$ as $26 \cdot 25 \cdot 24 \cdot 23!$ .

$\frac{26 \cdot 25 \cdot 24 \cdot 23!}{23! (48 \cdot 47 \cdot 46)}$

Step 7

Cancel the common factor of $26$ and $48$ .

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Step 7.1

Factor $2$ out of $26 \cdot 25 \cdot 24 \cdot 23!$ .

$\frac{2 (13 \cdot 25 \cdot 24 \cdot 23!)}{23! (48 \cdot 47 \cdot 46)}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $23! (48 \cdot 47 \cdot 46)$ .

$\frac{2 (13 \cdot 25 \cdot 24 \cdot 23!)}{2 (23! (24 \cdot 47 \cdot 46))}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (13 \cdot 25 \cdot 24 \cdot 23!)}{2 (23! (24 \cdot 47 \cdot 46))}$

Step 7.2.3

Rewrite the expression.

$\frac{13 \cdot 25 \cdot 24 \cdot 23!}{23! (24 \cdot 47 \cdot 46)}$

Step 8

Cancel the common factor of $24$ .

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Step 8.1

Cancel the common factor.

$\frac{13 \cdot 25 \cdot 24 \cdot 23!}{23! (24 \cdot 47 \cdot 46)}$

Step 8.2

Rewrite the expression.

$\frac{13 \cdot 25 \cdot 23!}{23! (47 \cdot 46)}$

Step 9

Cancel the common factor of $23!$ .

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Step 9.1

Cancel the common factor.

$\frac{13 \cdot 25 \cdot 23!}{23! (47 \cdot 46)}$

Step 9.2

Rewrite the expression.

$\frac{13 \cdot 25}{47 \cdot 46}$

Step 10

Multiply.

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Step 10.1

Multiply $13$ by $25$ .

$\frac{325}{47 \cdot 46}$

Step 10.2

Multiply $47$ by $46$ .

$\frac{325}{2162}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{325}{2162}$

Decimal Form:

$0.15032377 \dots$