Betty is making a sundae. She must randomly choose one flavour of ice cream (chocolate or vanilla or strawberry), one syrup (butterscotch or fudge) and one topping (cherry or banana or pineapple). What is the probability that she will choose a sundae with vanilla ice cream, fudge syrup and banana topping?
Problem 191
Pick one
Official solution
We systematically count rectangles by searching for groups of rectangles that are of similar size.
The largest rectangles in the diagram are all roughly the same size and overlap in pairs.
There are 3 of these; each is shaded black and shown below.
[[IMAGE0]]
Rectangle 2 (shown above) consists of 4 small rectangles.
We shade these rectangles black and label them , as shown below.
[[IMAGE1]]
Together, Rectangle 4 and Rectangle 5 (shown above) create Rectangle 8, shown below.
Similarly, Rectangle 6 and Rectangle 7 together create Rectangle 9, shown below.
[[IMAGE2]]
Finally, Rectangle 4 and Rectangle 6 (shown above) together create Rectangle 10, shown below.
Similarly, Rectangle 5 and Rectangle 7 together create Rectangle 11, shown below.
[[IMAGE3]]
There are no other rectangles that can be formed.
In total, there are 11 rectangles in the given diagram.