the Fundamental Counting Principle

Question

can be extended to count the ways to form different combinations of groupings. For example, if there are 4 dessert choices, 3 entrée choices and 2 appetizer choices, the number of dessert-entrée-appetizer combinations is 4x3x2 = 24. A restaurant advertises 120 dessert-entrée-appetizer combinations. If they have 5 entrée options and 3 appetizer options, how many dessert options do they have?

Answer 1

The total possible combinations equals the number of entree options * appetizer options * dessert options.

So:

120 = 5*3*x

120 = 15x

Solve for x to find the number of dessert options.