Now suppose there are Y different things. There are Y ways the first draw can occur. For each of the Y ways the first draw can occur, there are Y ways the second draw can occur, resulting in Y times Y, or Y2 sequences. For each of the Y2 sequences formed from 2 draws, there are Y ways the 3rd draw can occur forming Y3 sequences. Generalizing, there are YX sequences formed by drawing X times from Y different things with replacement. Example: The number of state license plates that can be made with 3 letters followed by 3 numbers is 26 x 26 x 26 x 10 x 10 x 10 = 263 x 103 = 17,576,000. From this one style of plate, there are many sequences. How many sequences of 5 things can be formed from 7 different things with replacement and order is important?
Now suppose there are Y different things. There are Y ways the first draw can occur. For each of the Y ways the first draw can occur, there are Y ways the second draw can occur, resulting in Y times Y, or Y2 sequences. For each of the Y2 sequences formed from 2 draws, there are Y ways the 3rd draw can occur forming Y3 sequences. Generalizing, there are YX sequences formed by drawing X times from Y different things with replacement. Example: The number of state license plates that can be made with 3 letters followed by 3 numbers is 26 x 26 x 26 x 10 x 10 x 10 = 263 x 103 = 17,576,000. From this one style of plate, there are many sequences. How many sequences of 5 things can be formed from 7 different things with replacement and order is important?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.1: Counting
Problem 1E: The Fundamental Counting Principle says that if one event can occur in m ways and a second event can...
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Now suppose there are Y different things. There are Y ways the first draw can occur. For each of the Y ways the first draw can occur, there are Y ways the second draw can occur, resulting in Y times Y, or Y2 sequences. For each of the Y2 sequences formed from 2 draws, there are Y ways the 3rd draw can occur forming Y3 sequences. Generalizing, there are YX sequences formed by drawing X times from Y different things with replacement. Example: The number of state license plates that can be made with 3 letters followed by 3 numbers is 26 x 26 x 26 x 10 x 10 x 10 = 263 x 103 = 17,576,000. From this one style of plate, there are many sequences. How many sequences of 5 things can be formed from 7 different things with replacement and order is important?
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