A restaurant menu contains four
starters, eight mains, and seven desserts. A meal consists of one starter, one
main, and one dessert. Work out the total number of
different meals that can be chosen from the menu.
This question is asking us to
calculate the number of different meals that can be chosen. That’s a meal with exactly one
starter, one main, and one dessert.
Now we probably don’t want to try
listing all possible combinations out. Instead, we can use the product
rule for counting the number of meals. To see where this comes from, first
imagine that a meal just consists of starters and main courses. We could use a sample space diagram
to list all the possible choices. We can put the starters along the
side and the eight mains along the top. We could then fill in the grid to
show starter one and main one, starter two and main one, and so on.
We’re actually only interested in
the total number of outcomes though. We have four rows of eight. That’s four multiplied by eight,
which is 32. That means there’s 32 different
ways to choose a starter and a main from four starters and eight mains.
We can then extend this idea to
include desserts. There are four ways of choosing a
starter, eight ways of choosing a main course, and seven ways of choosing a
dessert. That’s four times eight times
seven, which is 224. There are 224 different meals that
can be chosen from the menu.