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

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).

Complete These Ordered Pairs: (0, ) (2, ) (-1, ) y=3x-1 (-1, ) (0, ) (1, ) 2x+y=3 (0, ) (-1, ) (1, ) y=2x+1

Solution:

Each ordered paid represents x and y: (x,y)

To calculate y, you can plug in x.

If y=3x-1, then the given values of x will result in the pairs (0,-1) (2,5) (-1,-4).

If y=3-2x, then the given values of x will result in the pairs (-1,5) (0,3) (1,1).

If y=2x+1, then the given values of x will result in the pairs (0,1) (-1,-1) (1,3).