Finite Math Examples

${}_{17}C_{10}$

Step 1

Evaluate

${}_{17}C_{10}$ using the formula

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

$\frac{17!}{(17 - 10)! 10!}$

Step 2

Subtract

$10$ from

$17$ .

$\frac{17!}{(7)! 10!}$

Step 3

Simplify

$\frac{17!}{(7)! 10!}$ .

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Step 3.1

Rewrite

$17!$ as

$17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10!$ .

$\frac{17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10!}{(7)! 10!}$

Step 3.2

Cancel the common factor of

$10!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10!}{(7)! 10!}$

Step 3.2.2

Rewrite the expression.

$\frac{17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{(7)!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$17$ by

$16$ .

$\frac{272 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{(7)!}$

Step 3.3.2

Multiply

$272$ by

$15$ .

$\frac{4080 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{(7)!}$

Step 3.3.3

Multiply

$4080$ by

$14$ .

$\frac{57120 \cdot 13 \cdot 12 \cdot 11}{(7)!}$

Step 3.3.4

Multiply

$57120$ by

$13$ .

$\frac{742560 \cdot 12 \cdot 11}{(7)!}$

Step 3.3.5

Multiply

$742560$ by

$12$ .

$\frac{8910720 \cdot 11}{(7)!}$

Step 3.3.6

Multiply

$8910720$ by

$11$ .

$\frac{98017920}{(7)!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$(7)!$ to

$7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{98017920}{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.4.2.1

Multiply

$7$ by

$6$ .

$\frac{98017920}{42 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$42$ by

$5$ .

$\frac{98017920}{210 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$210$ by

$4$ .

$\frac{98017920}{840 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.4

Multiply

$840$ by

$3$ .

$\frac{98017920}{2520 \cdot 2 \cdot 1}$

Step 3.4.2.5

Multiply

$2520$ by

$2$ .

$\frac{98017920}{5040 \cdot 1}$

Step 3.4.2.6

Multiply

$5040$ by

$1$ .

$\frac{98017920}{5040}$

Step 3.5

Divide

$98017920$ by

$5040$ .

$19448$