Finite Math Examples

${}_{5}C_{1}$

Step 1

Evaluate ${}_{5}C_{1}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{5!}{(5 - 1)! 1!}$

Step 2

Subtract $1$ from $5$ .

$\frac{5!}{(4)! 1!}$

Step 3

Simplify $\frac{5!}{(4)! 1!}$ .

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Step 3.1

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

$\frac{5 \cdot 4!}{(4)! 1!}$

Step 3.2

Cancel the common factor of $4!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{5 \cdot 4!}{(4)! 1!}$

Step 3.2.2

Rewrite the expression.

$\frac{5}{1!}$

Step 3.3

Expand $1!$ to $1$ .

$\frac{5}{1}$

Step 3.4

Divide $5$ by $1$ .

$5$