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e other bag will have at least 4 tiles worth 1 point. ther bag.

e other bag will have at least 4 tiles worth 1 point. ther bag.

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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All four parts of this question refer to the following scrabble tiles. You do not need to understand the game of scrabble to answer the question. All you need to know is that it is played with tiles. Each tile has one letter on it, and a point value in the bottom right hand corner (e.g. "C" is worth 3 points). CO₁ MP OS T Note that there are some repeated tiles. For example the two S tiles are identical. For the first 3 parts of the question we place all of the above tiles into a bag. ON S Two tiles showing different letters are taken from the bag and a 2-element set is formed containing the two letters on the tiles. How many sets can be formed in this way? (Examples of sets that can be formed in this way include {C, M} and {N, T}) Two tiles are selected from the bag and a 2-element multiset is formed containing the letters on the tiles. How many multisets can be formed in this way? 31 (Examples of multisets that can be formed in this way include {C, M} and {0,0}.) 28 A tile is taken from the bag and left aside, and then another tile is taken from the bag. An ordered pair is formed whose first coordinate is the letter on the first tile and whose second coordinate is the letter on the second tile. How many possible ordered pairs can be formed in this way? 59 (Examples of ordered pairs that can be formed in this way include (M, C) and (I, I).)
Transcribed Image Text:All four parts of this question refer to the following scrabble tiles. You do not need to understand the game of scrabble to answer the question. All you need to know is that it is played with tiles. Each tile has one letter on it, and a point value in the bottom right hand corner (e.g. "C" is worth 3 points). CO₁ MP OS T Note that there are some repeated tiles. For example the two S tiles are identical. For the first 3 parts of the question we place all of the above tiles into a bag. ON S Two tiles showing different letters are taken from the bag and a 2-element set is formed containing the two letters on the tiles. How many sets can be formed in this way? (Examples of sets that can be formed in this way include {C, M} and {N, T}) Two tiles are selected from the bag and a 2-element multiset is formed containing the letters on the tiles. How many multisets can be formed in this way? 31 (Examples of multisets that can be formed in this way include {C, M} and {0,0}.) 28 A tile is taken from the bag and left aside, and then another tile is taken from the bag. An ordered pair is formed whose first coordinate is the letter on the first tile and whose second coordinate is the letter on the second tile. How many possible ordered pairs can be formed in this way? 59 (Examples of ordered pairs that can be formed in this way include (M, C) and (I, I).)
Suppose that the pictured tiles get split between two bags. Which of the following statements follows from the pigeonhole principle? ⒸOne bag will contain at least 5 tiles worth 1 point, the other bag will have at most 4 tiles worth 1 point. OBoth bags will contain at least 4 tiles worth 1 point. OOne bag will have more tiles in it than the other. One bag will contain at least 5 tiles worth 1 point, the other bag will have at least 4 tiles worth 1 point. OOne bag will have more points on its tiles than the other bag. OBoth bags must contain a tile with the letter O on it.
Transcribed Image Text:Suppose that the pictured tiles get split between two bags. Which of the following statements follows from the pigeonhole principle? ⒸOne bag will contain at least 5 tiles worth 1 point, the other bag will have at most 4 tiles worth 1 point. OBoth bags will contain at least 4 tiles worth 1 point. OOne bag will have more tiles in it than the other. One bag will contain at least 5 tiles worth 1 point, the other bag will have at least 4 tiles worth 1 point. OOne bag will have more points on its tiles than the other bag. OBoth bags must contain a tile with the letter O on it.
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