In this problem, a \"word\" is any string of seven (7) letters of the English al

Question

In this problem, a "word" is any string of seven (7) letters of the English alphabet, 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 3. 5^26, etc. in your final answers; no need to use calculators to compute such powers. How many words are there? How many words end with the letter T? How many words begin with R and end with T? How many words begin with A or B? How many words begin with A or end with B? How many words begin with A or B and end with A or B? How many words begin with A or B or end with A or B? How many words begin with AAB in some order? How many words have no vowels? How many words have exactly one vowel?

Explanation / Answer

1. 26 7 ( we need fill seven places with 26 letters where repeated is allowed)

2. 26 6 ( we need fill six places with 26 letters where repeated is allowed)

3. 26 5 ( we need fill five places with 26 letters where repeated is allowed)

4. 26 6+26 6 (( we need fill six places with 26 letters where repeated is allowed when the word starts with A or B)

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