Finite Math Examples

${}_{15}C_{3}$

Step 1

Evaluate

${}_{15}C_{3}$ using the formula

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

$\frac{15!}{(15 - 3)! 3!}$

Step 2

Subtract

$3$ from

$15$ .

$\frac{15!}{(12)! 3!}$

Step 3

Simplify

$\frac{15!}{(12)! 3!}$ .

Tap for more steps...

Step 3.1

Rewrite

$15!$ as

$15 \cdot 14 \cdot 13 \cdot 12!$ .

$\frac{15 \cdot 14 \cdot 13 \cdot 12!}{(12)! 3!}$

Step 3.2

Cancel the common factor of

$12!$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{15 \cdot 14 \cdot 13 \cdot 12!}{(12)! 3!}$

Step 3.2.2

Rewrite the expression.

$\frac{15 \cdot 14 \cdot 13}{3!}$

$\frac{15 \cdot 14 \cdot 13}{3!}$

Step 3.3

Simplify the numerator.

Tap for more steps...

Step 3.3.1

Multiply

$15$ by

$14$ .

$\frac{210 \cdot 13}{3!}$

Step 3.3.2

Multiply

$210$ by

$13$ .

$\frac{2730}{3!}$

$\frac{2730}{3!}$

Step 3.4

Simplify the denominator.

Tap for more steps...

Step 3.4.1

Expand

$3!$ to

$3 \cdot 2 \cdot 1$ .

$\frac{2730}{3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$3 \cdot 2 \cdot 1$ .

Tap for more steps...

Step 3.4.2.1

Multiply

$3$ by

$2$ .

$\frac{2730}{6 \cdot 1}$

Step 3.4.2.2

Multiply

$6$ by

$1$ .

$\frac{2730}{6}$

$\frac{2730}{6}$

$\frac{2730}{6}$

Step 3.5

Divide

$2730$ by

$6$ .

$455$

$455$

${}_{15}C_{3}$

(

(

)

)

|

|

[

[

]

]

√

√





≥

≥





















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

.

.

%

%



=

=









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