Finite Math Examples

11 C 2

${}_{11}C_{2}$

Step 1

Evaluate

11 C 2

${}_{11}C_{2}$ using the formula

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

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

\frac{11!}{(11 - 2)! 2!}

$\frac{11!}{(11 - 2)! 2!}$

Step 2

Subtract

2

$2$ from

11

$11$ .

\frac{11!}{(9)! 2!}

$\frac{11!}{(9)! 2!}$

Step 3

Simplify

\frac{11!}{(9)! 2!}

$\frac{11!}{(9)! 2!}$ .

Tap for more steps...

Step 3.1

Rewrite

11!

$11!$ as

11 \cdot 10 \cdot 9!

$11 \cdot 10 \cdot 9!$ .

\frac{11 \cdot 10 \cdot 9!}{(9)! 2!}

$\frac{11 \cdot 10 \cdot 9!}{(9)! 2!}$

Step 3.2

Cancel the common factor of

9!

$9!$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{11 \cdot 10 \cdot 9!}{(9)! 2!}$

Step 3.2.2

Rewrite the expression.

$\frac{11 \cdot 10}{2!}$

$\frac{11 \cdot 10}{2!}$

Step 3.3

Multiply

$11$ by

$10$ .

$\frac{110}{2!}$

Step 3.4

Simplify the denominator.

Tap for more steps...

Step 3.4.1

Expand

$2!$ to

$2 \cdot 1$ .

$\frac{110}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{110}{2}$

$\frac{110}{2}$

Step 3.5

Divide

$110$ by

$2$ .

$55$

$55$

${}_{11}C_{2}$

(

(

)

)

|

|

[

[

]

]

√

√





≥

≥





















7

7

8

8

9

9













≤

≤





















4

4

5

5

6

6

/

/

^

^

×

×

>

>

α

α

µ

µ













1

1

2

2

3

3

-

-

+

+

÷

÷

<

<

σ

σ









!

!



,

,

0

0

.

.

%

%



=

=









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