CAIE S1 2016 November — Question 6 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2016
SessionNovember
Marks3
TopicPermutations & Arrangements
TypeArrangements with grouped categories

6 Find the number of ways all 10 letters of the word COPENHAGEN can be arranged so that
  1. the vowels ( \(\mathrm { A } , \mathrm { E } , \mathrm { O }\) ) are together and the consonants ( \(\mathrm { C } , \mathrm { G } , \mathrm { H } , \mathrm { N } , \mathrm { P }\) ) are together, [3]
  2. the Es are not next to each other. Four letters are selected from the 10 letters of the word COPENHAGEN.
  3. Find the number of different selections if the four letters must contain the same number of Es and Ns with at least one of each.