4C4: 4 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 4C4:
4 CHOOSE 4 = 1
where,
4 is the total number of distinct elements (n),
4 is the the number of elements drawn or choosen at a time (k),
1 is the total number of possible combination (C).
4C4 Points to Remember:
4C4 is the type of nCr or nCk problem. The below 4 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 4 distinct elements without considering the order of elements.
Solved Example: :
what is 4 choose 4?
step 1 Address the input parameters and observe what to be found:
Input values:
Total number of distinct elements (n) = 4
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 4 distinct elements without considering the order of elements.
step 2 Find the factorial of 4:
4! = 1 x 2 x 3 x 4
step 3 Find the factorial of 4:
4! = 1 x 2 x 3 x 4
step 4 Find the factorial of difference between 4 and 4:
(4 - 4)! = 0!
0! = 1
step 5 Apply the values of 4!, 4! and 0! in the nCk formula:
nCk = n!/k! (n - k)!
4C4 =4!/4! x 0!
=1 x 2 x 3 x 4/(1 x 2 x 3 x 4) x (1)
step 6 Simplify the above 4C4 equation:
=1 x 2 x 3 x 4/(1 x 2 x 3 x 4) x (1)
= 1/1
= 1/1
4C4 = 1
Hence,
4 choose 4 equals to 1