Exercise 9

Consider all 5 letter “words” made from the letters $a$ through $h$. (Recall, words are just strings of letters, not necessarily actual English words.)

1. How many of these words are there total?

2. How many of these words contain no repeated letters?

3. How many of these words start with the sub-word “aha”?

4. How many of these words either start with “aha” or end with “bah” or both?

5. How many of the words containing no repeats also do not contain the sub-word “bad”?