# 5C2: 5 CHOOSE 2

5C2: 5 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 5C2:**

5 CHOOSE 2 = 10

__where,__

5 is the total number of distinct elements (n),

2 is the the number of elements drawn or choosen at a time (k),

10 is the total number of possible combination (C).

**5C2 Points to Remember:**

- 5 CHOOSE 2 can also be denoted as 5C2.
- Draw 2 out of 5 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 10 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 10 events.

## How-to find nCk: 5 CHOOSE 2?

5C2 is the type of nCr or nCk problem. The below 5 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 5 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 5 choose 2?

step 1 Address the input parameters and observe what to be found:

__Input values:__

Total number of distinct elements (n) = 5

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 5 distinct elements without considering the order of elements.

step 2 Find the factorial of 5:

5! = 1 x 2 x 3 x 4 x 5

step 3 Find the factorial of 2:

2! = 1 x 2

step 4 Find the factorial of difference between 5 and 2:

(5 - 2)! = 3!

3! = 1 x 2 x 3

step 5 Apply the values of 5!, 2! and 3! in the nCk formula:

nCk = n!/k! (n - k)!

5C2 =5!/2! x 3!

=1 x 2 x 3 x 4 x 5/(1 x 2) x (1 x 2 x 3)

step 6 Simplify the above 5C2 equation:

=1 x 2 x 3 x 4 x 5/(1 x 2) x (1 x 2 x 3)

= 4 x 5/2

= 20/2

5C2 = 10

Hence,

5 choose 2 equals to 10