Relevant definitions for this exercise:
THE PRODUCT RULE: “Suppose that a procedure can be broken down into a sequence of two tasks. If there are n1 ways to do the first task and for each of these ways of doing the first task, there are n2 ways to do the second task, then there are n1n2 ways to do the procedure.”
THE SUM RULE: “If a task can be done either in one of n1 ways or in one of n2 ways, where none of the set of n1 ways is the same as any of the set of n2 ways, then there are n1 +n2 ways to do the task.”
The definitions were taken from the textbook Discrete Mathematics and its Applications by Rosen.
Now, let’s describe the solution to the problem in a similar way to the principles above.
Every shirt can be made in 12 colors. For each of the 12 colors, a shirt it can be made for males or females. And for every 12 colors and for every male or female type, a shirt can be made in three different sizes.
It follows that we must apply the product rule. Notice the similarity in the way we wrote the problem and the way that the product rule is stated. Also, notice the difference between how we stated the problem and how the sum rule is stated.
Answer:
By the product rule, 12*2*3=72 different types of shirts are made.
Related exercises:
- How many bit strings are there of length eight?
- How many different three-letter initials with none of the letters repeated can people have?
- There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit?
- How many different three-letter initials are there that begin with an A?
- A multiple-choice test contains 10 questions. There are four possible answers for each question
- Six different airlines fly from New York to Denver and seven fly from Denver to San Francisco. How many different pairs of airlines can you choose on which to book a trip from New York to San Francisco via Denver, when you pick an airline for the flight to Denver and an airline for the continuation flight to San Francisco?
