Finite Math Examples

52 C 4

${}_{52}C_{4}$

Step 1

Evaluate

52 C 4

${}_{52}C_{4}$ using the formula

n C r = \frac{n!}{(n - r)! r!}

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

\frac{52!}{(52 - 4)! 4!}

$\frac{52!}{(52 - 4)! 4!}$

Step 2

Subtract

4

$4$ from

52

$52$ .

\frac{52!}{(48)! 4!}

$\frac{52!}{(48)! 4!}$

Step 3

Simplify

\frac{52!}{(48)! 4!}

$\frac{52!}{(48)! 4!}$ .

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Step 3.1

Rewrite

52!

$52!$ as

52 \cdot 51 \cdot 50 \cdot 49 \cdot 48!

$52 \cdot 51 \cdot 50 \cdot 49 \cdot 48!$ .

\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48!}{(48)! 4!}

$\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48!}{(48)! 4!}$

Step 3.2

Cancel the common factor of

48!

$48!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48!}{(48)! 4!}$

Step 3.2.2

Rewrite the expression.

$\frac{52 \cdot 51 \cdot 50 \cdot 49}{4!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$52$ by

$51$ .

$\frac{2652 \cdot 50 \cdot 49}{4!}$

Step 3.3.2

Multiply

$2652$ by

$50$ .

$\frac{132600 \cdot 49}{4!}$

Step 3.3.3

Multiply

$132600$ by

$49$ .

$\frac{6497400}{4!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$4!$ to

$4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{6497400}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$4$ by

$3$ .

$\frac{6497400}{12 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$12$ by

$2$ .

$\frac{6497400}{24 \cdot 1}$

Step 3.4.2.3

Multiply

$24$ by

$1$ .

$\frac{6497400}{24}$

Step 3.5

Divide

$6497400$ by

$24$ .

$270725$