4C4: 4 choose 4 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 4 elements at a time from 8 distinct elements without considering the order of elements.

**nCk of 4C4:**

4 CHOOSE 4 = 1

__where,__

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

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

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

**4C4 Points to Remember:**

- 4 CHOOSE 4 can also be denoted as 4C4.
- Draw 4 out of 4 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 1 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 1 events.

CHOOSE

4C4 is the type of nCr or nCk problem. The below 4 choose 4 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 4 elements at a time from 4 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 4 choose 4?

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) = 4

__What to be found:__

Find the total number of possible combinations while choosing 4 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 4:

4! = 1 x 2 x 3 x 4

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

(4 - 4)! = 0!

0! = 1

step 5 Apply the values of 4!, 4! and 0! in the nCk formula:

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

4C4 =4!/4! x 0!

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

step 6 Simplify the above 4C4 equation:

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

= 1/1

= 1/1

4C4 = 1

Hence,

4 choose 4 equals to 1