Finite Math Examples

${}_{2}C_{1}$

Step 1

Evaluate ${}_{2}C_{1}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{2!}{(2 - 1)! 1!}$

Step 2

Subtract $1$ from $2$ .

$\frac{2!}{(1)! 1!}$

Step 3

Simplify $\frac{2!}{(1)! 1!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

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

$\frac{2 \cdot 1}{(1)! 1!}$

Step 3.1.2

Multiply $2$ by $1$ .

$\frac{2}{(1)! 1!}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Raise $(1)!$ to the power of $1$ .

$\frac{2}{{(1)!}^{1} 1!}$

Step 3.2.2

Raise $1!$ to the power of $1$ .

$\frac{2}{{(1)!}^{1} {1!}^{1}}$

Step 3.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2}{{(1)!}^{1 + 1}}$

Step 3.2.4

Add $1$ and $1$ .

$\frac{2}{{(1)!}^{2}}$

Step 3.3

Simplify the denominator.

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Step 3.3.1

Expand $(1)!$ to $1$ .

$\frac{2}{1^{2}}$

Step 3.3.2

One to any power is one.

$\frac{2}{1}$

Step 3.4

Divide $2$ by $1$ .

$2$