8C3: 8 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 8C3:**

8 CHOOSE 3 = 56

__where,__

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

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

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

**8C3 Points to Remember:**

- 8 CHOOSE 3 can also be denoted as 8C3.
- Draw 3 out of 8 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 56 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 56 events.

CHOOSE

8C3 is the type of nCr or nCk problem. The below 8 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 8 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 8 choose 3?

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

__Input values:__

Total number of distinct elements (n) = 8

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 8 distinct elements without considering the order of elements.

step 2 Find the factorial of 8:

8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

step 3 Find the factorial of 3:

3! = 1 x 2 x 3

step 4 Find the factorial of difference between 8 and 3:

(8 - 3)! = 5!

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

step 5 Apply the values of 8!, 3! and 5! in the nCk formula:

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

8C3 =8!/3! x 5!

=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/(1 x 2 x 3) x (1 x 2 x 3 x 4 x 5)

step 6 Simplify the above 8C3 equation:

=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/(1 x 2 x 3) x (1 x 2 x 3 x 4 x 5)

= 6 x 7 x 8/6

= 336/6

8C3 = 56

Hence,

8 choose 3 equals to 56