Finite Math Examples

${}_{6}C_{4}$

Step 1

Evaluate ${}_{6}C_{4}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{6!}{(6 - 4)! 4!}$

Step 2

Subtract $4$ from $6$ .

$\frac{6!}{(2)! 4!}$

Step 3

Simplify $\frac{6!}{(2)! 4!}$ .

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Step 3.1

Rewrite $6!$ as $6 \cdot 5 \cdot 4!$ .

$\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}$

Step 3.2

Cancel the common factor of $4!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}$

Step 3.2.2

Rewrite the expression.

$\frac{6 \cdot 5}{(2)!}$

Step 3.3

Multiply $6$ by $5$ .

$\frac{30}{(2)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

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

$\frac{30}{2 \cdot 1}$

Step 3.4.2

Multiply $2$ by $1$ .

$\frac{30}{2}$

Step 3.5

Divide $30$ by $2$ .

$15$