Finite Math Examples

${}_{500}C_{2} \cdot 0.6$

Step 1

Evaluate ${}_{500}C_{2}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{500!}{(500 - 2)! 2!} \cdot 0.6$

Step 2

Subtract $2$ from $500$ .

$\frac{500!}{(498)! 2!} \cdot 0.6$

Step 3

Simplify $\frac{500!}{(498)! 2!}$ .

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Step 3.1

Rewrite $500!$ as $500 \cdot 499 \cdot 498!$ .

$\frac{500 \cdot 499 \cdot 498!}{(498)! 2!} \cdot 0.6$

Step 3.2

Cancel the common factor of $498!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{500 \cdot 499 \cdot 498!}{(498)! 2!} \cdot 0.6$

Step 3.2.2

Rewrite the expression.

$\frac{500 \cdot 499}{2!} \cdot 0.6$

Step 3.3

Multiply $500$ by $499$ .

$\frac{249500}{2!} \cdot 0.6$

Step 3.4

Simplify the denominator.

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Step 3.4.1

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

$\frac{249500}{2 \cdot 1} \cdot 0.6$

Step 3.4.2

Multiply $2$ by $1$ .

$\frac{249500}{2} \cdot 0.6$

Step 3.5

Divide $249500$ by $2$ .

$124750 \cdot 0.6$

Step 4

Multiply $124750$ by $0.6$ .

$74850$