# 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.

For values other than 6 choose 2, use this below tool:
CHOOSE

## 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 