CAIE S1 2023 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionJune
TopicCombinations & Selection

6 In a group of 25 people there are 6 swimmers, 8 cyclists and 11 runners. Each person competes in only one of these sports. A team of 7 people is selected from these 25 people to take part in a competition.
  1. Find the number of different ways in which the team of 7 can be selected if it consists of exactly 1 swimmer, at least 4 cyclists and at most 2 runners.
    For another competition, a team of 9 people consists of 2 swimmers, 3 cyclists and 4 runners. The team members stand in a line for a photograph.
  2. How many different arrangements are there of the 9 people if the swimmers stand together, the cyclists stand together and the runners stand together?
  3. How many different arrangements are there of the 9 people if none of the cyclists stand next to each other?
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.