12C5: 12 choose 5 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 5 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 12C5:
12 CHOOSE 5 = 792
where,
12 is the total number of distinct elements (n),
5 is the the number of elements drawn or choosen at a time (k),
792 is the total number of possible combination (C).
12C5 Points to Remember:
12C5 is the type of nCr or nCk problem. The below 12 choose 5 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 5 elements at a time from 12 distinct elements without considering the order of elements.
Solved Example: :
what is 12 choose 5?
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) = 5
What to be found:
Find the total number of possible combinations while choosing 5 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 5:
5! = 1 x 2 x 3 x 4 x 5
step 4 Find the factorial of difference between 12 and 5:
(12 - 5)! = 7!
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
step 5 Apply the values of 12!, 5! and 7! in the nCk formula:
nCk = n!/k! (n - k)!
12C5 =12!/5! x 7!
=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 (1 x 2 x 3 x 4 x 5 x 6 x 7)
step 6 Simplify the above 12C5 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 (1 x 2 x 3 x 4 x 5 x 6 x 7)
= 8 x 9 x 10 x 11 x 12/120
= 95040/120
12C5 = 792
Hence,
12 choose 5 equals to 792