12. As a special treat, Sammy is allowed to eat five sweets from his very large jar which contains many sweets of each of three flavours - Lemon, Orange and Strawberry. He wants to eat his five sweets in such a way that no two consecutive sweets have the same flavour.
In how many ways can he do this?
A 32
B 48
C 72
D 108
E 162
Solution
B Sammy has a choice of 3 flavours for the first sweet that he eats. Each of the other sweets he eats cannot be the same flavour as the sweet he has just eaten. So he has a choice of 2 flavours for each of these four sweets. So the total number of ways that he can make his choices is $3 \times 2 \times 2 \times 2 \times 2=48$.