Taken for a ride...
One day, since three motorbikes have become part of the Tan family, the family of six (Mr Tan, Mrs Tan, Benedict, Bob, Brenda and Brian) decided to go for a joy ride on their motorbikes, with exactly two on each one.
However, the restriction is that the two females (Mrs Tan and Brenda) do not ride motorbikes (like what many of you might expect). The four guys are however free to decide among themselves who to ride the motorbikes. How many arrangements are there?
The answer is 144.
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1 solution
First we arrange Mrs Tan and Brenda. There are only two places on each motorcycle (the driver and the pillion) and since the two ladies cannot be the ones riding, both have to be pillion riders. To arrange the two ladies would be simply 3 P 2 = 3 × 2 = 6 ways as it is only a matter of which motorcycle they ride on.
All we need to do now is to arrange the four guys. With four places left (3 riders and 1 pillion) and since there is no restriction here, we have 4! = 24 ways. By Multiplication Principle, there are 6 × 2 4 = 1 4 4 ways.