# 6C2: 6 CHOOSE 2

6C2: 6 choose 2 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 2 elements at a time from 8 distinct elements without considering the order of elements.

**nCk of 6C2:**

6 CHOOSE 2 = 15

__where,__

6 is the total number of distinct elements (n),

2 is the the number of elements drawn or choosen at a time (k),

15 is the total number of possible combination (C).

**6C2 Points to Remember:**

- 6 CHOOSE 2 can also be denoted as 6C2.
- Draw 2 out of 6 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 15 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 15 events.

## How-to find nCk: 6 CHOOSE 2?

6C2 is the type of nCr or nCk problem. The below 6 choose 2 work with steps help users to understand the combinations nCk formula, input parameters and how to find how many possible combinations/events occur while drawing 2 elements at a time from 6 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 6 choose 2?

step 1 Address the input parameters and observe what to be found:

__Input values:__

Total number of distinct elements (n) = 6

The number of elements drawn at a time (k) = 2

__What to be found:__

Find the total number of possible combinations while choosing 2 elements at a time from 6 distinct elements without considering the order of elements.

step 2 Find the factorial of 6:

6! = 1 x 2 x 3 x 4 x 5 x 6

step 3 Find the factorial of 2:

2! = 1 x 2

step 4 Find the factorial of difference between 6 and 2:

(6 - 2)! = 4!

4! = 1 x 2 x 3 x 4

step 5 Apply the values of 6!, 2! and 4! in the nCk formula:

nCk = n!/k! (n - k)!

6C2 =6!/2! x 4!

=1 x 2 x 3 x 4 x 5 x 6/(1 x 2) x (1 x 2 x 3 x 4)

step 6 Simplify the above 6C2 equation:

=1 x 2 x 3 x 4 x 5 x 6/(1 x 2) x (1 x 2 x 3 x 4)

= 5 x 6/2

= 30/2

6C2 = 15

Hence,

6 choose 2 equals to 15