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1. Consider arranging flags along the length of a flagpole. Rectangular flags come in six different colors and triangular flags come in two colors (different from the colors of the rectangular flags). The top flag must be triangular. In how many different ways can three to five flags be arranged on the pole a. if repetition of colors is allowed? b. if repetition of colors is not allowed?

1. Consider arranging flags along the length of a flagpole. Rectangular flags come in six different colors and triangular flags come in two colors (different from the colors of the rectangular flags). The top flag must be triangular. In how many different ways can three to five flags be arranged on the pole a. if repetition of colors is allowed? b. if repetition of colors is not allowed?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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determine who will give a gift to whom. In how many ways can this be done if exactly four staff members draw their own name? 1. Consider arranging flags along the length of a flagpole. Rectangular flags come in six different colors and triangular flags come in two colors (different from the colors of the rectangular flags). The top flag must be triangular. In how many different ways can three to five flags be arranged on the pole a. if repetition of colors is allowed? b. if repetition of colors is not allowed? 2. In how many ways can twenty 1000-peso bills be given away to four of ten people where each of the four receives at least one 5. A sports store sells tennis racquets of six different brands: Wilson, Prince, Babolat, Dunlop, Yonex and Head. In how many ways can you purchase four racquets so that you purchase must include a Wilson or a Prince tennis racquet? 6. Define a recurrence relation and all necessary initial conditions for the following problem: A string of n Christmas lights are to be created using green, red and clear bulbs. In how many ways can this be done so that no two clear bulbs are next to each other? 1000-peso bill? 3. Ten national leaders are to be seated at a round table at a summit. If the presidents of the US and Russia do not wish to be seated next to each other, in how many ways can this be done? 7. Solve the recurrence relation A, = 4 A2- 3.An-1 subject to the initial conditions A, = 5 and A, = 10. 4. The 25 staff members of an office decide to hold a Kris Kringle to celebrate the holidays and draw names written on slips of paper to
Transcribed Image Text:determine who will give a gift to whom. In how many ways can this be done if exactly four staff members draw their own name? 1. Consider arranging flags along the length of a flagpole. Rectangular flags come in six different colors and triangular flags come in two colors (different from the colors of the rectangular flags). The top flag must be triangular. In how many different ways can three to five flags be arranged on the pole a. if repetition of colors is allowed? b. if repetition of colors is not allowed? 2. In how many ways can twenty 1000-peso bills be given away to four of ten people where each of the four receives at least one 5. A sports store sells tennis racquets of six different brands: Wilson, Prince, Babolat, Dunlop, Yonex and Head. In how many ways can you purchase four racquets so that you purchase must include a Wilson or a Prince tennis racquet? 6. Define a recurrence relation and all necessary initial conditions for the following problem: A string of n Christmas lights are to be created using green, red and clear bulbs. In how many ways can this be done so that no two clear bulbs are next to each other? 1000-peso bill? 3. Ten national leaders are to be seated at a round table at a summit. If the presidents of the US and Russia do not wish to be seated next to each other, in how many ways can this be done? 7. Solve the recurrence relation A, = 4 A2- 3.An-1 subject to the initial conditions A, = 5 and A, = 10. 4. The 25 staff members of an office decide to hold a Kris Kringle to celebrate the holidays and draw names written on slips of paper to
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