Finite Math Examples

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

Step 1

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

$\frac{48 \cdot 47 \cdot 46 \cdot 45!}{3! \cdot 45!}$

Step 2

Cancel the common factor of $45!$ .

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Step 2.1

Cancel the common factor.

$\frac{48 \cdot 47 \cdot 46 \cdot 45!}{3! \cdot 45!}$

Step 2.2

Rewrite the expression.

$\frac{48 \cdot 47 \cdot 46}{3!}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $48$ by $47$ .

$\frac{2256 \cdot 46}{3!}$

Step 3.2

Multiply $2256$ by $46$ .

$\frac{103776}{3!}$

Step 4

Simplify the denominator.

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Step 4.1

Expand $3!$ to $3 \cdot 2 \cdot 1$ .

$\frac{103776}{3 \cdot 2 \cdot 1}$

Step 4.2

Multiply $3 \cdot 2 \cdot 1$ .

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Step 4.2.1

Multiply $3$ by $2$ .

$\frac{103776}{6 \cdot 1}$

Step 4.2.2

Multiply $6$ by $1$ .

$\frac{103776}{6}$

Step 5

Divide $103776$ by $6$ .

$17296$