6C6: 6 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 6C6:
6 CHOOSE 6 = 1
where,
6 is the total number of distinct elements (n),
6 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).
6C6 Points to Remember:
6C6 is the type of nCr or nCk problem. The below 6 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 6 distinct elements without considering the order of elements.
Solved Example: :
what is 6 choose 6?
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) = 6
What to be found:
Find the total number of possible combinations while choosing 6 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 6:
6! = 1 x 2 x 3 x 4 x 5 x 6
step 4 Find the factorial of difference between 6 and 6:
(6 - 6)! = 0!
0! = 1
step 5 Apply the values of 6!, 6! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
6C6 =6!/6! x 0!
=1 x 2 x 3 x 4 x 5 x 6/(1 x 2 x 3 x 4 x 5 x 6) x (1)
step 6 Simplify the above 6C6 equation:
=1 x 2 x 3 x 4 x 5 x 6/(1 x 2 x 3 x 4 x 5 x 6) x (1)
= 1/1
= 1/1
6C6 = 1
Hence,
6 choose 6 equals to 1