To determine the number of combinations possible with 5 letters, we first need to clarify if we’re referring to combinations without repetition or combinations with repetition.
If we assume the letters are unique and we’re only using them once, the number of combinations can be calculated using the formula for combinations, which is
C(n, r) = n! / [r!(n – r)!], where n is the total number of items to choose from, and r is the number of items to choose.
In this case, if we take 5 unique letters, the number of ways to choose all 5 letters at once (that is, r = 5) is:
C(5, 5) = 5! / [5!(5 – 5)!] = 1
This means there’s only 1 way to choose all 5 letters together.
However, if we’re talking about the number of possible arrangements or permutations of these 5 letters, we would use the permutation formula, which is P(n, r) = n! / (n – r)!. In this case, we can arrange 5 letters in:
P(5, 5) = 5! = 120
So, depending on whether we’re talking about combinations or permutations, the answer differs significantly. If we refer to just combinations of choosing from a set of 5 letters, there’s 1 way to choose them all. But if we consider how we can arrange those letters, there are 120 permutations available.