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