Finite Math Examples

${}_{7}C_{3}$

Step 1

Evaluate

${}_{7}C_{3}$ using the formula

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

$\frac{7!}{(7 - 3)! 3!}$

Step 2

Subtract

$3$ from

$7$ .

$\frac{7!}{(4)! 3!}$

Step 3

Simplify

$\frac{7!}{(4)! 3!}$ .

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Step 3.1

Rewrite

$7!$ as

$7 \cdot 6 \cdot 5 \cdot 4!$ .

$\frac{7 \cdot 6 \cdot 5 \cdot 4!}{(4)! 3!}$

Step 3.2

Cancel the common factor of

$4!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{7 \cdot 6 \cdot 5 \cdot 4!}{(4)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{7 \cdot 6 \cdot 5}{3!}$

$\frac{7 \cdot 6 \cdot 5}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$7$ by

$6$ .

$\frac{42 \cdot 5}{3!}$

Step 3.3.2

Multiply

$42$ by

$5$ .

$\frac{210}{3!}$

$\frac{210}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{210}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{210}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{210}{6}$

$\frac{210}{6}$

$\frac{210}{6}$

Step 3.5

Divide

$210$ by

$6$ .

$35$

$35$

${}_{7}C_{3}$

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