5C4: 5 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 5C4:
5 CHOOSE 4 = 5
where,
5 is the total number of distinct elements (n),
4 is the the number of elements drawn or choosen at a time (k),
5 is the total number of possible combination (C).
5C4 Points to Remember:
5C4 is the type of nCr or nCk problem. The below 5 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 5 distinct elements without considering the order of elements.
Solved Example: :
what is 5 choose 4?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 5
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 5 distinct elements without considering the order of elements.
step 2 Find the factorial of 5:
5! = 1 x 2 x 3 x 4 x 5
step 3 Find the factorial of 4:
4! = 1 x 2 x 3 x 4
step 4 Find the factorial of difference between 5 and 4:
(5 - 4)! = 1!
1! = 1
step 5 Apply the values of 5!, 4! and 1! in the nCk formula:
nCk = n!/k! (n - k)!
5C4 =5!/4! x 1!
=1 x 2 x 3 x 4 x 5/(1 x 2 x 3 x 4) x (1)
step 6 Simplify the above 5C4 equation:
=1 x 2 x 3 x 4 x 5/(1 x 2 x 3 x 4) x (1)
= 5/1
= 5/1
5C4 = 5
Hence,
5 choose 4 equals to 5