6C1: 6 choose 1 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 1 elements at a time from 8 distinct elements without considering the order of elements.

**nCk of 6C1:**

6 CHOOSE 1 = 6

__where,__

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

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

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

**6C1 Points to Remember:**

- 6 CHOOSE 1 can also be denoted as 6C1.
- Draw 1 out of 6 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.

CHOOSE

6C1 is the type of nCr or nCk problem. The below 6 choose 1 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 1 elements at a time from 6 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 6 choose 1?

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

__Input values:__

Total number of distinct elements (n) = 6

The number of elements drawn at a time (k) = 1

__What to be found:__

Find the total number of possible combinations while choosing 1 elements at a time from 6 distinct elements without considering the order of elements.

step 2 Find the factorial of 6:

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

step 3 Find the factorial of 1:

1! = 1

step 4 Find the factorial of difference between 6 and 1:

(6 - 1)! = 5!

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

step 5 Apply the values of 6!, 1! and 5! in the nCk formula:

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

6C1 =6!/1! x 5!

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

step 6 Simplify the above 6C1 equation:

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

Hence,

6 choose 1 equals to 6