# 9C6: 9 CHOOSE 6 9C6: 9 choose 6 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 6 elements at a time from 8 distinct elements without considering the order of elements.

nCk of 9C6:
9 CHOOSE 6 = 84
where,
9 is the total number of distinct elements (n),
6 is the the number of elements drawn or choosen at a time (k),
84 is the total number of possible combination (C).

9C6 Points to Remember:

• 9 CHOOSE 6 can also be denoted as 9C6.
• Draw 6 out of 9 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
• In 84 possible combinations, AB and BA are not considered as different events.
• AB and BA considered as a single combination in 84 events.

For values other than 9 choose 6, use this below tool:
CHOOSE

## How-to find nCk: 9 CHOOSE 6?

9C6 is the type of nCr or nCk problem. The below 9 choose 6 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 6 elements at a time from 9 distinct elements without considering the order of elements.

Solved Example: :
what is 9 choose 6?

step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 9
The number of elements drawn at a time (k) = 6

What to be found:
Find the total number of possible combinations while choosing 6 elements at a time from 9 distinct elements without considering the order of elements.

step 2 Find the factorial of 9:
9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9

step 3 Find the factorial of 6:
6! = 1 x 2 x 3 x 4 x 5 x 6

step 4 Find the factorial of difference between 9 and 6:
(9 - 6)! = 3!
3! = 1 x 2 x 3

step 5 Apply the values of 9!, 6! and 3! in the nCk formula:
nCk = n!/k! (n - k)!
9C6 =9!/6! x 3!

=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9/(1 x 2 x 3 x 4 x 5 x 6) x (1 x 2 x 3)

step 6 Simplify the above 9C6 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9/(1 x 2 x 3 x 4 x 5 x 6) x (1 x 2 x 3)

= 7 x 8 x 9/6
= 504/6

9C6 = 84

Hence,
9 choose 6 equals to 84 