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Unformatted text preview: Practice Midterm Solutions 1. How many four-letter words with no repeated letters can you form from the 26 letters of the alphabet? (Note that a word here need not be in the dictionary.) Solution. We select the letters of our word in the natural order (from left to right). There are 26 choices for the letter at the first (leftmost) position in the word. After that there are only 25 remaining possibilities for the second letter. Then we have 24 choices for the third one, and finally 23 possibilities for the last letter in the word. By the multiplication principle we conclude that the total number of such words is 26 25 24 23 = 358800 . It was not necessary to evaluate the above product. The answer can also be written as P (26 , 4), because we are selecting 4 objects from a set of 10 objects and the order of selection is important. See page 788 in the book. Again we have P (26 , 4) = 26 25 24 23 . 1 2. Assume that P ( A ) = 0 . 4 , P ( B ) = 0 . 4 , and P ( A S B ) = 0 . 7 . Find P ( A T B ) and P ( A c T B...
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This note was uploaded on 07/14/2008 for the course MATH 3C taught by Professor Schonmann during the Winter '07 term at UCLA.
- Winter '07