CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2 · Question 5(a)(ii)

A bus has 13 seats for passengers. Eight passengers boarded the bus before it left the terminal.

At the first stop, no passengers will get off the bus but there are eight other persons waiting to board the same bus. Among those waiting are three friends who must sit together. Determine the number of possible groups of five of the waiting passengers that can join the bus.