CAIE S1 2006 June — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2006
SessionJune
TopicPermutations & Arrangements
TypeSeating arrangements with constraints

4
\includegraphics[max width=\textwidth, alt={}, center]{14e8a601-2180-4491-9336-cafd262f2596-3_277_682_274_733} The diagram shows the seating plan for passengers in a minibus, which has 17 seats arranged in 4 rows. The back row has 5 seats and the other 3 rows have 2 seats on each side. 11 passengers get on the minibus.
  1. How many possible seating arrangements are there for the 11 passengers?
  2. How many possible seating arrangements are there if 5 particular people sit in the back row? Of the 11 passengers, 5 are unmarried and the other 6 consist of 3 married couples.
  3. In how many ways can 5 of the 11 passengers on the bus be chosen if there must be 2 married couples and 1 other person, who may or may not be married?