13C6: 13 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 13C6:
13 CHOOSE 6 = 1716
where,
13 is the total number of distinct elements (n),
6 is the the number of elements drawn or choosen at a time (k),
1716 is the total number of possible combination (C).
13C6 Points to Remember:
13C6 is the type of nCr or nCk problem. The below 13 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 13 distinct elements without considering the order of elements.
Solved Example: :
what is 13 choose 6?
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) = 6
What to be found:
Find the total number of possible combinations while choosing 6 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 6:
6! = 1 x 2 x 3 x 4 x 5 x 6
step 4 Find the factorial of difference between 13 and 6:
(13 - 6)! = 7!
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
step 5 Apply the values of 13!, 6! and 7! in the nCk formula:
nCk = n!/k! (n - k)!
13C6 =13!/6! 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 x 13/(1 x 2 x 3 x 4 x 5 x 6) x (1 x 2 x 3 x 4 x 5 x 6 x 7)
step 6 Simplify the above 13C6 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 (1 x 2 x 3 x 4 x 5 x 6 x 7)
= 8 x 9 x 10 x 11 x 12 x 13/720
= 1235520/720
13C6 = 1716
Hence,
13 choose 6 equals to 1716