Finite Math Examples

10 C 3

${}_{10}C_{3}$

Step 1

Evaluate

10 C 3

${}_{10}C_{3}$ using the formula

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

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

\frac{10!}{(10 - 3)! 3!}

$\frac{10!}{(10 - 3)! 3!}$

Step 2

Subtract

3

$3$ from

10

$10$ .

\frac{10!}{(7)! 3!}

$\frac{10!}{(7)! 3!}$

Step 3

Simplify

\frac{10!}{(7)! 3!}

$\frac{10!}{(7)! 3!}$ .

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Step 3.1

Rewrite

10!

$10!$ as

10 \cdot 9 \cdot 8 \cdot 7!

$10 \cdot 9 \cdot 8 \cdot 7!$ .

\frac{10 \cdot 9 \cdot 8 \cdot 7!}{(7)! 3!}

$\frac{10 \cdot 9 \cdot 8 \cdot 7!}{(7)! 3!}$

Step 3.2

Cancel the common factor of

7!

$7!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{10 \cdot 9 \cdot 8 \cdot 7!}{(7)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{10 \cdot 9 \cdot 8}{3!}$

$\frac{10 \cdot 9 \cdot 8}{3!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$10$ by

$9$ .

$\frac{90 \cdot 8}{3!}$

Step 3.3.2

Multiply

$90$ by

$8$ .

$\frac{720}{3!}$

$\frac{720}{3!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{720}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{720}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{720}{6}$

$\frac{720}{6}$

$\frac{720}{6}$

Step 3.5

Divide

$720$ by

$6$ .

$120$

$120$

${}_{10}C_{3}$

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