Suppose that A is a set of 8 (distinct) symbols and consider strings (i.e. sequences) over A.
How can I calculate the number of strings of length 5 which at least one symbol occurs two or more times. I started by calculating the total number of strings of length 5 by doing $8^5$ ( since we have 8 choices for each number) and then I subtracted the amount of strings of length 5 that do not have any repetition ($ 8\times 7\times 6\times 5 \times 4$) and I got the wrong answer. I think this is because my logic is wrong. Can someone help me?
Ok so it turns out my answer was correct and my professor was mistaken. The answer is 26048. The way I got to this number is explained in my question.