CAIE S1 2017 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2017
SessionJune
TopicPermutations & Arrangements
TypeArrangements with identical objects

6 A library contains 4 identical copies of book \(A , 2\) identical copies of book \(B\) and 5 identical copies of book \(C\). These 11 books are arranged on a shelf in the library.
  1. Calculate the number of different arrangements if the end books are either both book \(A\) or both book \(B\).
  2. Calculate the number of different arrangements if all the books \(A\) are next to each other and none of the books \(B\) are next to each other.