There are 6 candidates running in a Presidential primary. After each primary, two of the candidates will withdraw, except for the last one, when the winner becomes the nominee. (a) The first primary has all 6 candidates. In how many ways could the 6 candidates finish the race? (b) The second primary will only have the top 4 finishers from the first race. How many ways could the 4 candidates finish the second race? (c) The third primary only has the 2 remaining candidates. How many ways could this race finish?
There are 6 candidates running in a Presidential primary. After each primary, two of the candidates will withdraw, except for the last one, when the winner becomes the nominee. (a) The first primary has all 6 candidates. In how many ways could the 6 candidates finish the race? (b) The second primary will only have the top 4 finishers from the first race. How many ways could the 4 candidates finish the second race? (c) The third primary only has the 2 remaining candidates. How many ways could this race finish?
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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There are 6 candidates running in a Presidential primary. After each primary, two of the candidates will withdraw, except for the last one, when the winner becomes the nominee.
(a) The first primary has all 6 candidates. In how many ways could the 6 candidates finish the race?
(b) The second primary will only have the top 4 finishers from the first race. How many ways could the
4 candidates finish the second race?
(c) The third primary only has the 2 remaining candidates. How many ways could this race finish?
(d) Use your answers to parts (a)-(c) to calculate the total number of ways the primaries could play out (that is, how many different ways could the candidates win/lose in the primary)?
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