8C8: 8 choose 8 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 8 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 8C8:
8 CHOOSE 8 = 1
where,
8 is the total number of distinct elements (n),
8 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).
8C8 Points to Remember:
8C8 is the type of nCr or nCk problem. The below 8 choose 8 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 8 elements at a time from 8 distinct elements without considering the order of elements.
Solved Example: :
what is 8 choose 8?
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) = 8
What to be found:
Find the total number of possible combinations while choosing 8 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 8:
8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
step 4 Find the factorial of difference between 8 and 8:
(8 - 8)! = 0!
0! = 1
step 5 Apply the values of 8!, 8! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
8C8 =8!/8! x 0!
=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 7 x 8) x (1)
step 6 Simplify the above 8C8 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 7 x 8) x (1)
= 1/1
= 1/1
8C8 = 1
Hence,
8 choose 8 equals to 1