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Question: in this problem a quotwordquot is any string of seven...

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Problem 1. (50 10 5 points) In this problem, a word is any string of seven (7) letters of the English alpha- bet, with repeated letters allowed. Also, we will consider Y to be a vowel Provide a brief justification for each of your answers (no more than five lines or so), explaining which counting rules you used and what your thought process was. Finally, feel free to have expressions of the form 26 etc. in your final answers; no need to use calculators to compute such powers. 1. How many words are there? 2. How many words end with the letter T? 3. How many words begin with R and end with T? 4. How many words begin with A or B? 5. How many words begin with A or end with B? 6. How many words begin with A or B and end with A or B? 7. How many words begin with A or B or end with A or B? 8. How many words begin with AAB in some order? 9. How many words have no vowels? 10. How many words have exactly one vowel?

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