# 3C1: 3 CHOOSE 1 3C1: 3 choose 1 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 1 elements at a time from 8 distinct elements without considering the order of elements.

nCk of 3C1:
3 CHOOSE 1 = 3
where,
3 is the total number of distinct elements (n),
1 is the the number of elements drawn or choosen at a time (k),
3 is the total number of possible combination (C).

3C1 Points to Remember:

• 3 CHOOSE 1 can also be denoted as 3C1.
• Draw 1 out of 3 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
• In 3 possible combinations, AB and BA are not considered as different events.
• AB and BA considered as a single combination in 3 events.

For values other than 3 choose 1, use this below tool:
CHOOSE

## How-to find nCk: 3 CHOOSE 1?

3C1 is the type of nCr or nCk problem. The below 3 choose 1 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 1 elements at a time from 3 distinct elements without considering the order of elements.

Solved Example: :
what is 3 choose 1?

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) = 1

What to be found:
Find the total number of possible combinations while choosing 1 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 1:
1! = 1

step 4 Find the factorial of difference between 3 and 1:
(3 - 1)! = 2!
2! = 1 x 2

step 5 Apply the values of 3!, 1! and 2! in the nCk formula:
nCk = n!/k! (n - k)!
3C1 =3!/1! x 2!

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

step 6 Simplify the above 3C1 equation:
=1 x 2 x 3/(1) x (1 x 2)

Hence,
3 choose 1 equals to 3 