CAIE S1 2013 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionJune
TopicPermutations & Arrangements
TypePeople arrangements in lines

6 Four families go to a theme park together. Mr and Mrs Lin take their 2 children. Mr O'Connor takes his 2 children. Mr and Mrs Ahmed take their 3 children. Mrs Burton takes her son. The 14 people all have to go through a turnstile one at a time to enter the theme park.
  1. In how many different orders can the 14 people go through the turnstile if each family stays together?
  2. In how many different orders can the 8 children and 6 adults go through the turnstile if no two adults go consecutively? Once inside the theme park, the children go on the roller-coaster. Each roller-coaster car holds 3 people.
  3. In how many different ways can the 8 children be divided into two groups of 3 and one group of 2 to go on the roller-coaster?