A computer game has five difficulty levels. In each level you can choose among four different scenarios except for the first level, where you can choose among three scenarios only. How many different games are possible?
My answer is: $3\times 4 \times 4 \times 4 \times 4$
But the given answer is: $3+4 + 4 +4 + 4 =19$
How am I wrong?
The book apparently wanted to ask for the number of games, where there is no concept of advancing from one level to the next, since after all they didn't say there was. On the other hand your answer is correct if you consider a complete game to consist of playing every level in order.