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Suppose a Word is a String of 8 letters of the Alphabet with Repeated Letters Allowed: (5 points, 1 point each) Show all work. Do not Answer with just a Number. 1. How many words are there? 2. How many words end with the letter N? 3. How many words begin with R and end with N? 4. How many words start with A or B? 5. How many words begin with A or end with B

Friday, October 1st, 2010

Solution:

  1. If you have 26 choices for each letter in a word, then there are 26 such one-letter words, 262 two-letter words, 263 three-letter words, etc. There would be 268 eight-letter words.
  2. There would be 267 eight-letter words that end with the letter N, which is the same as the number of 7 letter words (just add “N” to the end of each seven-letter word.
  3. There would be 266 eight-letter words that begin with R and end with N (just add R to the front and N to the end of all six-letter words.
  4. There would be 2*267 eight-letter words that begin with an A or B (add A to the beginning of every seven-letter word, then add B to the beginning of every seven-letter word).
  5. There would be 2*267 eight-letter words that begin with A or end with B (add A to the beginning of every seven-letter word, then add B to the end of every 7 letter word).

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