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Nov 2015 p62 q4
2844
A group of 8 friends travels to the airport in two taxis, P and Q. Each taxi can take 4 passengers.
The 8 friends divide themselves into two groups of 4, one group for taxi P and one group for taxi Q, with Jon and Sarah travelling in the same taxi. Find the number of different ways in which this can be done.
Solution
Since Jon and Sarah must travel in the same taxi, we consider them as a single unit. This leaves us with 6 other friends to arrange.
First, choose 2 more friends to join Jon and Sarah in the same taxi. This can be done in \\(^6C_2\\) ways.
The remaining 4 friends automatically go into the other taxi. Thus, the number of ways to choose the groups is \\(^6C_2\\).
However, Jon and Sarah can be in either taxi P or taxi Q, so we multiply by 2 to account for both possibilities.
Therefore, the total number of ways is \\(^6C_2 \\times 2 = 15 \\times 2 = 30\\).