Combinations and Permutations

Question

Congratulations! You graduated and your family is planning a trip to europe. You have a choice between italy, ireland, france, and spain. You find that there are three airlines that offer good rates in europe. Also, you have to choose between five hotels in the city of your choice. How many different ways can you plan your trip making decisions about the country you plan to visit, the airline, and the hotel?

Answer 1

Savannah:

 

Repeated application of the "m times n" rule: "If a system requires two stages, if the first stage can be completed in m ways and if the second in n ways,   then the system can be completed in m times n ways."

 

Here the "system" (planning your trip) has three stages, countries (4), airlines (3) and hotels 5).  You can plan your trip in 4 times 3 times 5 ways. = 60 different ways.

 

Dr. G.