A cafe offers 3 main courses and 2 puddings. How many different two-course meals can be ordered?
Text description of the figure
A tree diagram. One starting point branches into three main courses, and each of those branches into two puddings, giving six paths in all.
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Draw a branch for each main course.
2The strategy
Start one branch per main course, then split each of those into one branch per pudding. The number of meals is the number of endings, not the number of lines.
3The full solution
Three mains, each splitting into two puddings, gives 3 x 2 = 6 endings.
Solution
The reliable way
Draw the tree. From the start there are three branches, one per main course. Each of those splits into two, one per pudding. That gives 3 x 2 = 6 complete paths, and each path is one meal. The transferable idea: the meals are the endings of the tree, not the branches you drew.
The elegant way
Two independent choices multiply: 3 x 2 = 6.
Why this is on the test: Adding instead of multiplying is the first and most persistent error in the counting strand, and a tree makes the multiplication visible.