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Unformatted text preview: Stat 230 - Assignment 1 Due in class on Friday, October 8, 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 4 white and 2 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 black and 4 white marbles? Check your answer for the case n = 2 . (c) In which of the arrangements in 1a (list them) is every white marble adjacent to at least one other white marble? (d) List the ways to arrange 2 black 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 white marbles.) (f) How many ways are there to arrange n black and 4 white marbles so that every white marble is adjacent to at least one other white marble? (Check that your answer agrees with part 1c.) (g) If 22 black and 4 white marbles are arranged at random, what is the probability that every white marble is adjacent to at least one other white marble?...
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