12C12: 12 choose 12 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 12 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 12C12:
12 CHOOSE 12 = 1
where,
12 is the total number of distinct elements (n),
12 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).
12C12 Points to Remember:
12C12 is the type of nCr or nCk problem. The below 12 choose 12 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 12 elements at a time from 12 distinct elements without considering the order of elements.
Solved Example: :
what is 12 choose 12?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 12
The number of elements drawn at a time (k) = 12
What to be found:
Find the total number of possible combinations while choosing 12 elements at a time from 12 distinct elements without considering the order of elements.
step 2 Find the factorial of 12:
12! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12
step 3 Find the factorial of 12:
12! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12
step 4 Find the factorial of difference between 12 and 12:
(12 - 12)! = 0!
0! = 1
step 5 Apply the values of 12!, 12! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
12C12 =12!/12! x 0!
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12/(1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12) x (1)
step 6 Simplify the above 12C12 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12/(1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12) x (1)
= 1/1
= 1/1
12C12 = 1
Hence,
12 choose 12 equals to 1