4C2: 4 CHOOSE 2

4C2: 4 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 4C2:
4 CHOOSE 2 = 6
where,
4 is the total number of distinct elements (n),
2 is the the number of elements drawn or choosen at a time (k),
6 is the total number of possible combination (C).

4C2 Points to Remember:

• 4 CHOOSE 2 can also be denoted as 4C2.
• Draw 2 out of 4 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
• In 6 possible combinations, AB and BA are not considered as different events.
• AB and BA considered as a single combination in 6 events.

4C2 is the type of nCr or nCk problem. The below 4 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 4 distinct elements without considering the order of elements.

Solved Example: :
what is 4 choose 2?

step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 4
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 4 distinct elements without considering the order of elements.

step 2 Find the factorial of 4:
4! = 1 x 2 x 3 x 4

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

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

step 5 Apply the values of 4!, 2! and 2! in the nCk formula:
nCk = n!/k! (n - k)!
4C2 =4!/2! x 2!

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

step 6 Simplify the above 4C2 equation:
=1 x 2 x 3 x 4/(1 x 2) x (1 x 2)

= 3 x 4/2
= 12/2

4C2 = 6

Hence,
4 choose 2 equals to 6