13C11: 13 CHOOSE 11
13C11: 13 choose 11 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 11 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 13C11:
13 CHOOSE 11 = 78
where,
13 is the total number of distinct elements (n),
11 is the the number of elements drawn or choosen at a time (k),
78 is the total number of possible combination (C).
13C11 Points to Remember:
- 13 CHOOSE 11 can also be denoted as 13C11.
- Draw 11 out of 13 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
- In 78 possible combinations, AB and BA are not considered as different events.
- AB and BA considered as a single combination in 78 events.
How-to find nCk: 13 CHOOSE 11?
13C11 is the type of nCr or nCk problem. The below 13 choose 11 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 11 elements at a time from 13 distinct elements without considering the order of elements.
Solved Example: :
what is 13 choose 11?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 13
The number of elements drawn at a time (k) = 11
What to be found:
Find the total number of possible combinations while choosing 11 elements at a time from 13 distinct elements without considering the order of elements.
step 2 Find the factorial of 13:
13! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13
step 3 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 4 Find the factorial of difference between 13 and 11:
(13 - 11)! = 2!
2! = 1 x 2
step 5 Apply the values of 13!, 11! and 2! in the nCk formula:
nCk = n!/k! (n - k)!
13C11 =13!/11! x 2!
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13/(1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11) x (1 x 2)
step 6 Simplify the above 13C11 equation:
=1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13/(1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11) x (1 x 2)
= 12 x 13/2
= 156/2
13C11 = 78
Hence,
13 choose 11 equals to 78