Assignment-09-F19-Counting1-Solution (1).pdf - Discrete...

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Discrete StructuresFall 2019Assignment-09SolutionProblem 1(a)How many words of 10 letters can you form, using the English alphabet? (there are 26 different letters, ofwhich 5 are vowels).
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(b)How many words of length 10 can you form, where no letter is repeated?
(c)How many words of length 8 can you form, where the first letter is the same as the last letter?
(d)How many words of length 8 can you form, which contain exactly one vowel?7
Problem 2A flag consists of a 1×3 rectangle, divided into three equal squares, each square being painted in one of 10 possiblecolors. Moreover, two adjacent squares cannot be painted with the same color. Finally, a flag may have a coloredcircle at the center of the middle square: in this case, the color of the circle must be different from the other colorsused to paint the squares. How many different flags can be obtained, following the rules above?

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