Finite Math Examples

6 C 4

${}_{6}C_{4}$

Step 1

Evaluate

6 C 4

${}_{6}C_{4}$ using the formula

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

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

\frac{6!}{(6 - 4)! 4!}

$\frac{6!}{(6 - 4)! 4!}$

Step 2

Subtract

4

$4$ from

6

$6$ .

\frac{6!}{(2)! 4!}

$\frac{6!}{(2)! 4!}$

Step 3

Simplify

\frac{6!}{(2)! 4!}

$\frac{6!}{(2)! 4!}$ .

Tap for more steps...

Step 3.1

Rewrite

6!

$6!$ as

6 \cdot 5 \cdot 4!

$6 \cdot 5 \cdot 4!$ .

\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}

$\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}$

Step 3.2

Cancel the common factor of

4!

$4!$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{6 \cdot 5 \cdot 4!}{(2)! 4!}$

Step 3.2.2

Rewrite the expression.

$\frac{6 \cdot 5}{(2)!}$

$\frac{6 \cdot 5}{(2)!}$

Step 3.3

Multiply

$6$ by

$5$ .

$\frac{30}{(2)!}$

Step 3.4

Simplify the denominator.

Tap for more steps...

Step 3.4.1

Expand

$(2)!$ to

$2 \cdot 1$ .

$\frac{30}{2 \cdot 1}$

Step 3.4.2

Multiply

$2$ by

$1$ .

$\frac{30}{2}$

$\frac{30}{2}$

Step 3.5

Divide

$30$ by

$2$ .

$15$

$15$

${}_{6}C_{4}$

(

(

)

)

|

|

[

[

]

]

√

√





≥

≥





















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

.

.

%

%



=

=









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