The combination of 5 items taken 5 at a time, often denoted as 5C5, is a concept in combinatorics. It represents the number of ways to choose 5 items from a set of 5 without considering the order of selection.
To calculate 5C5, we use the combination formula:
C(n, k) = n! / (k! * (n – k)!)
Where:
- n is the total number of items.
- k is the number of items to choose.
- ! denotes factorial, which is the product of all positive integers up to that number.
Plugging in the values for 5C5:
C(5, 5) = 5! / (5! * (5 – 5)!) = 5! / (5! * 0!)
Since 0! is defined as 1, the equation simplifies to:
C(5, 5) = 5! / (5! * 1) = 1
Therefore, there is only 1 way to choose all 5 items from a set of 5.