# 6C3: 6 CHOOSE 3

6C3: 6 choose 3 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 3 elements at a time from 8 distinct elements without considering the order of elements.

**nCk of 6C3:**

6 CHOOSE 3 = 20

__where,__

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

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

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

**6C3 Points to Remember:**

- 6 CHOOSE 3 can also be denoted as 6C3.
- Draw 3 out of 6 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 20 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 20 events.

## How-to find nCk: 6 CHOOSE 3?

6C3 is the type of nCr or nCk problem. The below 6 choose 3 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 3 elements at a time from 6 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 6 choose 3?

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) = 3

__What to be found:__

Find the total number of possible combinations while choosing 3 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 3:

3! = 1 x 2 x 3

step 4 Find the factorial of difference between 6 and 3:

(6 - 3)! = 3!

3! = 1 x 2 x 3

step 5 Apply the values of 6!, 3! and 3! in the nCk formula:

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

6C3 =6!/3! x 3!

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

step 6 Simplify the above 6C3 equation:

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

= 4 x 5 x 6/6

= 120/6

6C3 = 20

Hence,

6 choose 3 equals to 20