# 3C3: 3 CHOOSE 3 3C3: 3 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 3C3:
3 CHOOSE 3 = 1
where,
3 is the total number of distinct elements (n),
3 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).

3C3 Points to Remember:

• 3 CHOOSE 3 can also be denoted as 3C3.
• Draw 3 out of 3 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
• In 1 possible combinations, AB and BA are not considered as different events.
• AB and BA considered as a single combination in 1 events.

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

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

3C3 is the type of nCr or nCk problem. The below 3 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 3 distinct elements without considering the order of elements.

Solved Example: :
what is 3 choose 3?

step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 3
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 3 distinct elements without considering the order of elements.

step 2 Find the factorial of 3:
3! = 1 x 2 x 3

step 3 Find the factorial of 3:
3! = 1 x 2 x 3

step 4 Find the factorial of difference between 3 and 3:
(3 - 3)! = 0!
0! = 1

step 5 Apply the values of 3!, 3! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
3C3 =3!/3! x 0!

=1 x 2 x 3/(1 x 2 x 3) x (1)

step 6 Simplify the above 3C3 equation:
=1 x 2 x 3/(1 x 2 x 3) x (1)

= 1/1
= 1/1

3C3 = 1

Hence,
3 choose 3 equals to 1 