Finite Math Examples

${}_{7}C_{6}$

Step 1

Evaluate

${}_{7}C_{6}$ using the formula

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

$\frac{7!}{(7 - 6)! 6!}$

Step 2

Subtract

$6$ from

$7$ .

$\frac{7!}{(1)! 6!}$

Step 3

Simplify

$\frac{7!}{(1)! 6!}$ .

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Step 3.1

Rewrite

$7!$ as

$7 \cdot 6!$ .

$\frac{7 \cdot 6!}{(1)! 6!}$

Step 3.2

Cancel the common factor of

$6!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{7 \cdot 6!}{(1)! 6!}$

Step 3.2.2

Rewrite the expression.

$\frac{7}{(1)!}$

$\frac{7}{(1)!}$

Step 3.3

Expand

$(1)!$ to

$1$ .

$\frac{7}{1}$

Step 3.4

Divide

$7$ by

$1$ .

$7$

$7$

${}_{7}C_{6}$

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