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?
(A) $\frac{1}{18}$
(B) $\frac{1}{6}$
(C) $\frac{1}{8}$
(D) $\frac{1}{9}$
(E) $\frac{1}{12}$
Betty has 3 equally likely choices for the flavour of ice cream (chocolate or vanilla or strawberry). For each of these 3 choices, she has 2 equally likely choices for the syrup (butterscotch or fudge). Thus, Betty has $3 \times 2$ or 6 equally likely choices for the flavour and syrup of the sundae.

For each of these 6 choices, Betty has 3 equally likely choices for the topping (cherry or banana or pineapple).

This makes $6 \times 3$ or 18 equally likely choices for her sundae.

Since only 1 of these 18 choices is the sundae with vanilla ice cream, fudge syrup and banana topping, then the probability that Betty randomly chooses this sundae is $\frac{1}{18}$.

ANSWER: (A)