9C5: 9 choose 5 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 5 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 9C5:
9 CHOOSE 5 = 126
where,
9 is the total number of distinct elements (n),
5 is the the number of elements drawn or choosen at a time (k),
126 is the total number of possible combination (C).
9C5 Points to Remember:
9C5 is the type of nCr or nCk problem. The below 9 choose 5 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 5 elements at a time from 9 distinct elements without considering the order of elements.
Solved Example: :
what is 9 choose 5?
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) = 5
What to be found:
Find the total number of possible combinations while choosing 5 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 5:
5! = 1 x 2 x 3 x 4 x 5
step 4 Find the factorial of difference between 9 and 5:
(9 - 5)! = 4!
4! = 1 x 2 x 3 x 4
step 5 Apply the values of 9!, 5! and 4! in the nCk formula:
nCk = n!/k! (n - k)!
9C5 =9!/5! x 4!
=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 (1 x 2 x 3 x 4)
step 6 Simplify the above 9C5 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 (1 x 2 x 3 x 4)
= 6 x 7 x 8 x 9/24
= 3024/24
9C5 = 126
Hence,
9 choose 5 equals to 126