Finite Math Examples

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

Step 1

Evaluate ${}_{52}C_{4}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

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

Step 2

Subtract $4$ from $52$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factor of $48!$ .

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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 $24$ .

$270725$