# 5C1: 5 CHOOSE 1

5C1: 5 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 5C1:**

5 CHOOSE 1 = 5

__where,__

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

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

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

**5C1 Points to Remember:**

- 5 CHOOSE 1 can also be denoted as 5C1.
- Draw 1 out of 5 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 5 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 5 events.

## How-to find nCk: 5 CHOOSE 1?

5C1 is the type of nCr or nCk problem. The below 5 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 5 distinct elements without considering the order of elements.

__Solved Example:__ :

what is 5 choose 1?

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) = 1

__What to be found:__

Find the total number of possible combinations while choosing 1 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 1:

1! = 1

step 4 Find the factorial of difference between 5 and 1:

(5 - 1)! = 4!

4! = 1 x 2 x 3 x 4

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

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

5C1 =5!/1! x 4!

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

step 6 Simplify the above 5C1 equation:

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

Hence,

5 choose 1 equals to 5