4C3: 4 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 4C3:**

4 CHOOSE 3 = 4

__where,__

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

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

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

**4C3 Points to Remember:**

- 4 CHOOSE 3 can also be denoted as 4C3.
- Draw 3 out of 4 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 4 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 4 events.

CHOOSE

4C3 is the type of nCr or nCk problem. The below 4 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 4 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 4 choose 3?

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) = 3

__What to be found:__

Find the total number of possible combinations while choosing 3 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 3:

3! = 1 x 2 x 3

step 4 Find the factorial of difference between 4 and 3:

(4 - 3)! = 1!

1! = 1

step 5 Apply the values of 4!, 3! and 1! in the nCk formula:

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

4C3 =4!/3! x 1!

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

step 6 Simplify the above 4C3 equation:

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

= 4/1

= 4/1

4C3 = 4

Hence,

4 choose 3 equals to 4