This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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?...
View
Full
Document
 Fall '10
 MichaelLa
 Counting, Probability

Click to edit the document details