PREVNEXTSUBMITMenuResourcesGlossaryNotesClear and return to MenuSearch ResultsFilterSlide TextNotesSearch in:Check to includeSearch...TermsDefinitiondefinitionresourcessearchpauseplayreplaysubmitnextpreviousvolumethe fundamental counting principle examples example 1: sofia lives in toronto and is planning a trip to montreal. she would like to stop in ottawa along the way. checking the internet, she finds that she can take a bus, train, or two different flights from toronto to ottawa, then, she has a choice of train or bus from ottawa to montreal. how many ways can sofia travel from toronto to montreal? bus choices for the trip from toronto to ottawa tree diagram: bus train flight # 1 flight # 2 bus bus bus train train train train choices for the trip from ottawa to montreal sofia has 8 possible ways to travel from toronto to montreal 4 choices from toronto to ottawa 2 choices from ottawa to montreal = 8 possibilities example 2: until 1997, most license plates for passenger cars in the province of ontario had three numbers followed by three letters. how many different license plates are available in the province of ontario? number number number letter letter letter using the fundamental counting principle for multiplication: there are 17,576,000 possibilities example 3: maria is looking at stereos for her car in an electronic store. the store has six types of receivers, four types of players, and five types of speakers. how many different choices of stereos systems does this store offer? receivers players speakers using the fundamental counting principle for multiplication: there are 120 possibilities example 4: at a private school, students wear school uniforms. each student must wear either a white dress shirt, a blue dress shirt, or a white golf shirt. student must also wear dress pants in grey, black, or navy blue. how many variations are there of this uniform? first action: selecting a type of shirt second action: selecting a type of pants tree diagram: white dress shirt blue dress blue white golf shirt a shirt can be selected in three ways, whereas pants can be selected in three ways as well. by the fundamental counting principle, a complete uniform can be selected in: 3 = 9 possibilities black pants grey pants navy blue pants black pants grey pants navy blue pants black pants grey pants navy blue pants example 5: a new rule regarding footwear is introduced for the uniform in the previous example. it states that: “student must wear only black or blue shoes in a loafer or laced-up style; socks must be black, navy blue, white, grey or light blue.” now, how different styles of uniform are possible? first action: selecting a type of shirt (3 choices: white dress shirt, blue dress shirt and white golf shirt) second action: selecting a type of pants (3 choices: grey pants, black pants and navy blue pants) third action: selecting shoes (4 choices: black loafers, black laced-up, navy blue loafers, and navy blue laced-up) fourth action: selecting socks (5 choices: five different colours) shirt pants shoes socks using the fundamental counting principle for multiplication: there are 180 variations of different styles of uniform.