3C2: 3 CHOOSE 2

3C2: 3 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 3C2:
3 CHOOSE 2 = 3
where,
3 is the total number of distinct elements (n),
2 is the the number of elements drawn or choosen at a time (k),
3 is the total number of possible combination (C).

3C2 Points to Remember:

• 3 CHOOSE 2 can also be denoted as 3C2.
• Draw 2 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.

3C2 is the type of nCr or nCk problem. The below 3 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 3 distinct elements without considering the order of elements.

Solved Example: :
what is 3 choose 2?

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) = 2

What to be found:
Find the total number of possible combinations while choosing 2 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 2:
2! = 1 x 2

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

step 5 Apply the values of 3!, 2! and 1! in the nCk formula:
nCk = n!/k! (n - k)!
3C2 =3!/2! x 1!

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

step 6 Simplify the above 3C2 equation:
=1 x 2 x 3/(1 x 2) x (1)

= 3/1
= 3/1

3C2 = 3

Hence,
3 choose 2 equals to 3