13C13: 13 choose 13 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 13 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 13C13:
13 CHOOSE 13 = 1
where,
13 is the total number of distinct elements (n),
13 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).
13C13 Points to Remember:
13C13 is the type of nCr or nCk problem. The below 13 choose 13 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 13 elements at a time from 13 distinct elements without considering the order of elements.
Solved Example: :
what is 13 choose 13?
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) = 13
What to be found:
Find the total number of possible combinations while choosing 13 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 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 4 Find the factorial of difference between 13 and 13:
(13 - 13)! = 0!
0! = 1
step 5 Apply the values of 13!, 13! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
13C13 =13!/13! x 0!
=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 12 x 13) x (1)
step 6 Simplify the above 13C13 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 12 x 13) x (1)
= 1/1
= 1/1
13C13 = 1
Hence,
13 choose 13 equals to 1