Ten nominees for an award are seated at a round table at a banquet. (a) Three awardees are chosen. How many different sets of three winners are possible? (b) There is actually a ranking among the three awardees, with first, second, and third places winning different prizes. How many different ordered slates of three winners are possible? (c) After the winners are announced, one nominee remarks to another, "Isn't it in- teresting that none of the winners were sitting next to each other?" How many ways are there to pick a set of three winners from the table, none of whom are seated next to one another? For this problem, we don't care who comes in first, second, and third. Hint: Define A; as the set of all outcomes where nominees i and i+ 1 are both chosen. The bad outcomes are then |A₁ U A₂ U... U A10| which seems like too much to ask via PIE, but luckily most intersections are very easy to count. For example, A₁ A₂] = 1 (why?) and A₁ A3] = 0.

Ten nominees for an award are seated at a round table at a banquet. (a) Three awardees are chosen. How many different sets of three winners are possible? (b) There is actually a ranking among the three awardees, with first, second, and third places winning different prizes. How many different ordered slates of three winners are possible? (c) After the winners are announced, one nominee remarks to another, "Isn't it in- teresting that none of the winners were sitting next to each other?" How many ways are there to pick a set of three winners from the table, none of whom are seated next to one another? For this problem, we don't care who comes in first, second, and third. Hint: Define A; as the set of all outcomes where nominees i and i+ 1 are both chosen. The bad outcomes are then |A₁ U A₂ U... U A10| which seems like too much to ask via PIE, but luckily most intersections are very easy to count. For example, A₁ A₂] = 1 (why?) and A₁ A3] = 0.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.1: Counting

Problem 84E

See similar textbooks