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. "P" is worth 3 points). RE P. E T. ITQON TIJ0N Note that there are some repeated tiles. For example the two E tiles are identical. How many sets of two tiles can be selected from these tiles, if we insist that the two chosen tiles contain different letters? In how many ways can you form a multiset of 2 tiles from the ones pictured? Suppose that I take one tile from the word, and then take another tile. How many possible ordered pairs of tiles can I form in this way? Suppose that the pictured tiles get arranged into two piles. Which of the following statements follows from the pigeonhole principle? OBoth piles must contain a tile with the letter T on it. OBoth piles will contain at least 4 tiles worth 1 point. OOne pile will be bigger than the other. OOne pile will have more points on its tiles than the other pile. OOne pile will contain at least 5 tiles worth 1 point, the other pile will have at most 4 tiles worth 1 point. OOne pile will contain at least 5 tiles worth 1 point, the other pile will have at least 4 tiles worth 1 point.

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ISBN:9780470458365
Author:Erwin Kreyszig
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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. "P" is worth 3 points).
REPETLTLON
T. 10
3
1
1
1
1
Note that there are some repeated tiles. For example the two E tiles are identical.
How many sets of two tiles can be selected from these tiles, if we insist that the two chosen tiles contain different letters?
In how many ways can you form a multiset of 2 tiles from the ones pictured?
Suppose that I take one tile from the word, and then take another tile. How many possible ordered pairs of tiles can I form in this way?
Suppose that the pictured tiles get arranged into two piles. Which of the following statements follows from the pigeonhole principle?
OBoth piles must contain a tile with the letter T on it.
OBoth piles will contain at least 4 tiles worth 1 point.
OOne pile will be bigger than the other.
OOne pile will have more points on its tiles than the other pile.
OOne pile will contain at least 5 tiles worth 1 point, the other pile will have at most 4 tiles worth 1 point.
OOne pile will contain at least 5 tiles worth 1 point, the other pile will have at least 4 tiles worth 1 point.
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. "P" is worth 3 points). REPETLTLON T. 10 3 1 1 1 1 Note that there are some repeated tiles. For example the two E tiles are identical. How many sets of two tiles can be selected from these tiles, if we insist that the two chosen tiles contain different letters? In how many ways can you form a multiset of 2 tiles from the ones pictured? Suppose that I take one tile from the word, and then take another tile. How many possible ordered pairs of tiles can I form in this way? Suppose that the pictured tiles get arranged into two piles. Which of the following statements follows from the pigeonhole principle? OBoth piles must contain a tile with the letter T on it. OBoth piles will contain at least 4 tiles worth 1 point. OOne pile will be bigger than the other. OOne pile will have more points on its tiles than the other pile. OOne pile will contain at least 5 tiles worth 1 point, the other pile will have at most 4 tiles worth 1 point. OOne pile will contain at least 5 tiles worth 1 point, the other pile will have at least 4 tiles worth 1 point.
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