Finite Math Examples

7 C 1

${}_{7}C_{1}$

Step 1

Evaluate

7 C 1

${}_{7}C_{1}$ using the formula

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

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

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

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

Step 2

Subtract

1

$1$ from

7

$7$ .

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

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

Step 3

Simplify

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

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

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Step 3.1

Rewrite

7!

$7!$ as

7 \cdot 6!

$7 \cdot 6!$ .

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

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

Step 3.2

Cancel the common factor of

6!

$6!$ .

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Step 3.2.1

Cancel the common factor.

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

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

$1$ .

$7$

$7$

${}_{7}C_{1}$

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