Hi Julie! Here is an approach to solving both problems:
a. Firstly, there are 7 letters so there are 7! ways to arrange all the letters. Then, if we can treat A and E as a single group, we will now have 6 groups. There are 6! ways to arrange all of these groups. Since we can also swap A and E in their group because we do not care about order, there are 2 times the possibilities.
Thus our answer is: (6! * 2) / 7! = 2 / 7
b. For this part we can use an approach that is similar to part a. We can treat A, B, and C as one group. Now, we have 5 groups. There are 5! ways to arrange these groups. There are 7! ways to arrange the letters in total.
Thus our answer is: 5! / 7! = 1 / (6 * 7) = 1 / 42
