Final answer:
The number of possible strings from an alphabet where length is at most 'd' is calculated using the formula n⁰d. This formula considers each position in a string up to length 'd' and each position can be any of the 'n' characters in the alphabet.
Step-by-step explanation:
The number of possible strings of length at most 'd' from an alphabet with 'n' characters can be calculated by the formula n¹⁰d, which accounts for all different combinations for each position in the string for up to 'd' positions.
To explain further, for each position in the string, you can have any of the 'n' characters, meaning that for a string of length 1, there are 'n' possibilities. When you consider a string of length 2, each position can still be any of the 'n' characters, leading to n x n or n² combinations. This pattern continues, thus for a string of length 'd', the number of combinations becomes n⁰d (n raised to the power of d).
This calculation assumes repetitions are allowed and order does matter. If repetitions weren't allowed or order didn't matter, the calculation would be different. For example, the formula n! (n factorial) is used when calculating arrangements where order matters and each element is used once.