13C5: 13 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 13C5:
13 CHOOSE 5 = 1287
where,
13 is the total number of distinct elements (n),
5 is the the number of elements drawn or choosen at a time (k),
1287 is the total number of possible combination (C).
13C5 Points to Remember:
13C5 is the type of nCr or nCk problem. The below 13 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 13 distinct elements without considering the order of elements.
Solved Example: :
what is 13 choose 5?
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) = 5
What to be found:
Find the total number of possible combinations while choosing 5 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 5:
5! = 1 x 2 x 3 x 4 x 5
step 4 Find the factorial of difference between 13 and 5:
(13 - 5)! = 8!
8! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
step 5 Apply the values of 13!, 5! and 8! in the nCk formula:
nCk = n!/k! (n - k)!
13C5 =13!/5! x 8!
=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 (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8)
step 6 Simplify the above 13C5 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 (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8)
= 9 x 10 x 11 x 12 x 13/120
= 154440/120
13C5 = 1287
Hence,
13 choose 5 equals to 1287