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Unformatted text preview: Stat 230 - Assignment 1 Due in class on Wednesday, June 2, 2010 The first three questions consider the process of arranging coloured marbles in a row from left to right. Two marbles of the same colour are to be considered indistinguishable when counting arrangements. 1. (a) Suppose that there are 2 white and 4 black marbles. One way to arrange the marbles is . List all 15 ways to arrange these marbles. (b) What combinatorial number describes the number of ways to arrange n white and 4 black marbles? Check your answer for the case n = 2 . (c) In which of the arrangements in 1a (list them) is every black marble adjacent to at least one other black marble? (d) List the ways to arrange 2 white and 2 red marbles. (e) Explain why the lists in 1c and 1d have the same size? (Hint: Consider replacing each red marble with two consecutive black marbles.) (f) How many ways are there to arrange n white and 4 black marbles so that every black marble is adjacent to at least one other black marble? (Check that your answer agrees with part 1c.) (g) If 20 white and 4 black marbles are arranged at random, what is the probability that every black marble is adjacent to at least one other black marble?that every black marble is adjacent to at least one other black marble?...
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- Spring '10