12C6: 12 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 12C6:
12 CHOOSE 6 = 924
where,
12 is the total number of distinct elements (n),
6 is the the number of elements drawn or choosen at a time (k),
924 is the total number of possible combination (C).
12C6 Points to Remember:
12C6 is the type of nCr or nCk problem. The below 12 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 12 distinct elements without considering the order of elements.
Solved Example: :
what is 12 choose 6?
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) = 6
What to be found:
Find the total number of possible combinations while choosing 6 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 6:
6! = 1 x 2 x 3 x 4 x 5 x 6
step 4 Find the factorial of difference between 12 and 6:
(12 - 6)! = 6!
6! = 1 x 2 x 3 x 4 x 5 x 6
step 5 Apply the values of 12!, 6! and 6! in the nCk formula:
nCk = n!/k! (n - k)!
12C6 =12!/6! x 6!
=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 (1 x 2 x 3 x 4 x 5 x 6)
step 6 Simplify the above 12C6 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 (1 x 2 x 3 x 4 x 5 x 6)
= 7 x 8 x 9 x 10 x 11 x 12/720
= 665280/720
12C6 = 924
Hence,
12 choose 6 equals to 924