Finite Math Examples

${}_{52}C_{3}$

Step 1

Evaluate

${}_{52}C_{3}$ using the formula

${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{52!}{(52 - 3)! 3!}$

Step 2

Subtract

$3$ from

$52$ .

$\frac{52!}{(49)! 3!}$

Step 3

Simplify

$\frac{52!}{(49)! 3!}$ .

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Step 3.1

Rewrite

$52!$ as

$52 \cdot 51 \cdot 50 \cdot 49!$ .

$\frac{52 \cdot 51 \cdot 50 \cdot 49!}{(49)! 3!}$

Step 3.2

Cancel the common factor of

$49!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{52 \cdot 51 \cdot 50 \cdot 49!}{(49)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{52 \cdot 51 \cdot 50}{3!}$

$\frac{52 \cdot 51 \cdot 50}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$52$ by

$51$ .

$\frac{2652 \cdot 50}{3!}$

Step 3.3.2

Multiply

$2652$ by

$50$ .

$\frac{132600}{3!}$

$\frac{132600}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{132600}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{132600}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{132600}{6}$

$\frac{132600}{6}$

$\frac{132600}{6}$

Step 3.5

Divide

$132600$ by

$6$ .

$22100$

$22100$

${}_{52}C_{3}$

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