2025 SAJC P2 Q6

A group of \(8\) tourists \(–\) \(2\) married couples and \(4\) singles \(–\) travels to the airport in two taxis, \(X\) and \(Y\). Each taxi can take \(4\) passengers.

The \(8\) tourists divide themselves into two groups of \(4\), one group for taxi \(X\) and one group for taxi \(Y\).

1. Find the number of different ways in which this can be done if each married couple must travel together in the same taxi.[2]

Each taxi can take \(1\) passenger in the front and \(3\) passengers in the back (see diagram).

2. Find the number of seating arrangements so that each married couple sit next to each other at the back of the taxi.[3]