Question: A bit is a 0 or a 1. A bit string of length 5 is a sequence of 5 digits, all of which are

A bit is a 0 or a 1. A bit string of length 5 is a sequence of 5 digits, all of which are either 0 and 1. (a) How many bit strings of length 5 are there? (b) How many bit strings of length 5 or less are there? (Count the empty string of length zero also.) c. For the rest of your outfit, you have 8 shirts, 7 skirts, 4 pants, and 6 dresses. You want to select either a shirt to wear with a skirt or pants, or just a dress. How many outfits do you have to choose from? 54 How many strings of 4 lower case English letters are there that have the letter x in them somewhere? Here strings may use the same letter more than once. (Hint: It might be easier to first count the strings that don't have an x in them.) Your answer is: 4-letter ``words" are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions? (a) No condition is imposed. Your answer is: (b) No letter can be repeated in a word. Your answer is: (c) Each word must begin with the letter A. Your answer is: (d) The letter C must be at the end. Your answer is: (e) The second letter must be a vowel. Your answer is : Standard automobile license plates in a country display 2 numbers, followed repetition of letters and numbers is allowed.) Your answer is: 3 letters, followed by 2 numbers. How many different standard plates are possible in this system? (Assume

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