Finite Math Examples

${}_{10}C_{6}$

Step 1

Evaluate

${}_{10}C_{6}$ using the formula

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

$\frac{10!}{(10 - 6)! 6!}$

Step 2

Subtract

$6$ from

$10$ .

$\frac{10!}{(4)! 6!}$

Step 3

Simplify

$\frac{10!}{(4)! 6!}$ .

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Step 3.1

Rewrite

$10!$ as

$10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!$ .

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{(4)! 6!}$

Step 3.2

Cancel the common factor of

$6!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{(4)! 6!}$

Step 3.2.2

Rewrite the expression.

$\frac{10 \cdot 9 \cdot 8 \cdot 7}{(4)!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$10$ by

$9$ .

$\frac{90 \cdot 8 \cdot 7}{(4)!}$

Step 3.3.2

Multiply

$90$ by

$8$ .

$\frac{720 \cdot 7}{(4)!}$

Step 3.3.3

Multiply

$720$ by

$7$ .

$\frac{5040}{(4)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(4)!$ to

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

$\frac{5040}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

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

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Step 3.4.2.1

Multiply

$4$ by

$3$ .

$\frac{5040}{12 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$12$ by

$2$ .

$\frac{5040}{24 \cdot 1}$

Step 3.4.2.3

Multiply

$24$ by

$1$ .

$\frac{5040}{24}$

Step 3.5

Divide

$5040$ by

$24$ .

$210$