# 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.

For values other than 6 choose 3, use this below tool:
CHOOSE

## 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 