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

$1$ .

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

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

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

$1$ .

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

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

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.

$\frac{2}{1}$

$\frac{2}{1}$

Step 3.4

Divide

$2$ by

$1$ .

$2$

$2$

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

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$