12C3: 12 choose 3 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 3 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 12C3:
12 CHOOSE 3 = 220
where,
12 is the total number of distinct elements (n),
3 is the the number of elements drawn or choosen at a time (k),
220 is the total number of possible combination (C).
12C3 Points to Remember:
12C3 is the type of nCr or nCk problem. The below 12 choose 3 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 3 elements at a time from 12 distinct elements without considering the order of elements.
Solved Example: :
what is 12 choose 3?
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) = 3
What to be found:
Find the total number of possible combinations while choosing 3 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 3:
3! = 1 x 2 x 3
step 4 Find the factorial of difference between 12 and 3:
(12 - 3)! = 9!
9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
step 5 Apply the values of 12!, 3! and 9! in the nCk formula:
nCk = n!/k! (n - k)!
12C3 =12!/3! x 9!
=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 (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)
step 6 Simplify the above 12C3 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 (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)
= 10 x 11 x 12/6
= 1320/6
12C3 = 220
Hence,
12 choose 3 equals to 220