11C5: 11 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 11C5:
11 CHOOSE 5 = 462
where,
11 is the total number of distinct elements (n),
5 is the the number of elements drawn or choosen at a time (k),
462 is the total number of possible combination (C).
11C5 Points to Remember:
11C5 is the type of nCr or nCk problem. The below 11 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 11 distinct elements without considering the order of elements.
Solved Example: :
what is 11 choose 5?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 11
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 11 distinct elements without considering the order of elements.
step 2 Find the factorial of 11:
11! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11
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 11 and 5:
(11 - 5)! = 6!
6! = 1 x 2 x 3 x 4 x 5 x 6
step 5 Apply the values of 11!, 5! and 6! in the nCk formula:
nCk = n!/k! (n - k)!
11C5 =11!/5! x 6!
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11/(1 x 2 x 3 x 4 x 5) x (1 x 2 x 3 x 4 x 5 x 6)
step 6 Simplify the above 11C5 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11/(1 x 2 x 3 x 4 x 5) x (1 x 2 x 3 x 4 x 5 x 6)
= 7 x 8 x 9 x 10 x 11/120
= 55440/120
11C5 = 462
Hence,
11 choose 5 equals to 462