CAIE S1 2008 November — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2008
SessionNovember
TopicPermutations & Arrangements
TypeArrangements with identical objects
4 A builder is planning to build 12 houses along one side of a road. He will build 2 houses in style \(A\), 2 houses in style \(B , 3\) houses in style \(C , 4\) houses in style \(D\) and 1 house in style \(E\).
  1. Find the number of possible arrangements of these 12 houses.
  2. Road
    \(\square \square \square \square \square \square \square \square \square\)\(\square \square \square\)
    The 12 houses will be in two groups of 6 (see diagram). Find the number of possible arrangements if all the houses in styles \(A\) and \(D\) are in the first group and all the houses in styles \(B , C\) and \(E\) are in the second group.
  3. Four of the 12 houses will be selected for a survey. Exactly one house must be in style \(B\) and exactly one house in style \(C\). Find the number of ways in which these four houses can be selected.
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