# 5C3: 5 CHOOSE 3 5C3: 5 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 5C3:
5 CHOOSE 3 = 10
where,
5 is the total number of distinct elements (n),
3 is the the number of elements drawn or choosen at a time (k),
10 is the total number of possible combination (C).

5C3 Points to Remember:

• 5 CHOOSE 3 can also be denoted as 5C3.
• Draw 3 out of 5 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
• In 10 possible combinations, AB and BA are not considered as different events.
• AB and BA considered as a single combination in 10 events.

For values other than 5 choose 3, use this below tool:
CHOOSE

## How-to find nCk: 5 CHOOSE 3?

5C3 is the type of nCr or nCk problem. The below 5 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 5 distinct elements without considering the order of elements.

Solved Example: :
what is 5 choose 3?

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) = 3

What to be found:
Find the total number of possible combinations while choosing 3 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 3:
3! = 1 x 2 x 3

step 4 Find the factorial of difference between 5 and 3:
(5 - 3)! = 2!
2! = 1 x 2

step 5 Apply the values of 5!, 3! and 2! in the nCk formula:
nCk = n!/k! (n - k)!
5C3 =5!/3! x 2!

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

step 6 Simplify the above 5C3 equation:
=1 x 2 x 3 x 4 x 5/(1 x 2 x 3) x (1 x 2)

= 4 x 5/2
= 20/2

5C3 = 10

Hence,
5 choose 3 equals to 10 