Finite Math Examples

${}_{46}C_{6}$

Step 1

Evaluate

${}_{46}C_{6}$ using the formula

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

$\frac{46!}{(46 - 6)! 6!}$

Step 2

Subtract

$6$ from

$46$ .

$\frac{46!}{(40)! 6!}$

Step 3

Simplify

$\frac{46!}{(40)! 6!}$ .

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Step 3.1

Rewrite

$46!$ as

$46 \cdot 45 \cdot 44 \cdot 43 \cdot 42 \cdot 41 \cdot 40!$ .

$\frac{46 \cdot 45 \cdot 44 \cdot 43 \cdot 42 \cdot 41 \cdot 40!}{(40)! 6!}$

Step 3.2

Cancel the common factor of

$40!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{46 \cdot 45 \cdot 44 \cdot 43 \cdot 42 \cdot 41 \cdot 40!}{(40)! 6!}$

Step 3.2.2

Rewrite the expression.

$\frac{46 \cdot 45 \cdot 44 \cdot 43 \cdot 42 \cdot 41}{6!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

$46$ by

$45$ .

$\frac{2070 \cdot 44 \cdot 43 \cdot 42 \cdot 41}{6!}$

Step 3.3.2

Multiply

$2070$ by

$44$ .

$\frac{91080 \cdot 43 \cdot 42 \cdot 41}{6!}$

Step 3.3.3

Multiply

$91080$ by

$43$ .

$\frac{3916440 \cdot 42 \cdot 41}{6!}$

Step 3.3.4

Multiply

$3916440$ by

$42$ .

$\frac{164490480 \cdot 41}{6!}$

Step 3.3.5

Multiply

$164490480$ by

$41$ .

$\frac{6744109680}{6!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

Expand

$6!$ to

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

$\frac{6744109680}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

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

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Step 3.4.2.1

Multiply

$6$ by

$5$ .

$\frac{6744109680}{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$30$ by

$4$ .

$\frac{6744109680}{120 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply

$120$ by

$3$ .

$\frac{6744109680}{360 \cdot 2 \cdot 1}$

Step 3.4.2.4

Multiply

$360$ by

$2$ .

$\frac{6744109680}{720 \cdot 1}$

Step 3.4.2.5

Multiply

$720$ by

$1$ .

$\frac{6744109680}{720}$

Step 3.5

Divide

$6744109680$ by

$720$ .

$9366819$