13C4: 13 choose 4 work with steps provide the detailed information about what is the total number of possible combinations occur (nCk) while choosing 4 elements at a time from 8 distinct elements without considering the order of elements.
nCk of 13C4:
13 CHOOSE 4 = 715
where,
13 is the total number of distinct elements (n),
4 is the the number of elements drawn or choosen at a time (k),
715 is the total number of possible combination (C).
13C4 Points to Remember:
13C4 is the type of nCr or nCk problem. The below 13 choose 4 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 4 elements at a time from 13 distinct elements without considering the order of elements.
Solved Example: :
what is 13 choose 4?
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) = 4
What to be found:
Find the total number of possible combinations while choosing 4 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 4:
4! = 1 x 2 x 3 x 4
step 4 Find the factorial of difference between 13 and 4:
(13 - 4)! = 9!
9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
step 5 Apply the values of 13!, 4! and 9! in the nCk formula:
nCk = n!/k! (n - k)!
13C4 =13!/4! x 9!
=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 (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)
step 6 Simplify the above 13C4 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 (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)
= 10 x 11 x 12 x 13/24
= 17160/24
13C4 = 715
Hence,
13 choose 4 equals to 715