8C6: 8 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 8C6:
8 CHOOSE 6 = 28
where,
8 is the total number of distinct elements (n),
6 is the the number of elements drawn or choosen at a time (k),
28 is the total number of possible combination (C).
8C6 Points to Remember:
8C6 is the type of nCr or nCk problem. The below 8 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 8 distinct elements without considering the order of elements.
Solved Example: :
what is 8 choose 6?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 8
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 8 distinct elements without considering the order of elements.
step 2 Find the factorial of 8:
8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
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 8 and 6:
(8 - 6)! = 2!
2! = 1 x 2
step 5 Apply the values of 8!, 6! and 2! in the nCk formula:
nCk = n!/k! (n - k)!
8C6 =8!/6! x 2!
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/(1 x 2 x 3 x 4 x 5 x 6) x (1 x 2)
step 6 Simplify the above 8C6 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/(1 x 2 x 3 x 4 x 5 x 6) x (1 x 2)
= 7 x 8/2
= 56/2
8C6 = 28
Hence,
8 choose 6 equals to 28