Problem 2" (80 = 10*8 points) In this problem, a "word" is any string of nine capital letters of the English alphabet, with repeated letters allowed. Also, we will consider "Y" to be a vowel. As an example, COMPSCIEN is a word, but COMPUTER is not (as it consists of eight letters). Provide a brief justification for each of your answers (no more than five lines or so). State which counting You can give final expressions in the form 3.526, etc.; no need to use calculators to compute such powers. 1. How many words are there? 2. How many words end with the letter K? 3. How many words begin with A and end with A? 4. How many words begin with K or L? 5. How many words begin with K or end with 6. How many words begin with D or E and end with K or L? 7. How many words begin with F or G or end with T or Y? 8. How many words begin with the letters in DDAD in any order? rules you used and explain your thought process and reasoning. L? For example, DDADXXXXX and DADDYYYYY are two such words. 9. How many words have no vowels? 10. How many words start with two vowels and end with two vowels