The Fundamental Counting Principle
- the Fundamental Counting Principle says that if there are "a" items in set 1, and "b" items in set 2, and "c" items in set 3, etc, then the number of ways to choose one object from each set is a*b*c
- to solve any problem, find two things
- the number of "choices" you are making
- the number of "options" you have for each choice
Setting Lamps On Or Off
How many ways can you set 4 lamps, when each lamp can either be on or off?
Hiring People For A Job
How many ways can 2 job vacancies be filled by 8 applicants?
Choosing A Meal At A Restaurant
How many different meal combos can be created with 6 main courses, 3 side dishes, and 3 desserts?
How You Can Easily Have 1000 Outfits
If you have 10 different shirts, 10 different pairs of pants, and 10 different pairs of shoes, you have 1000 different outfits.
License Plates With ABC-123
How many license plates exist with the format ABC-123?
License Plates With No Repetition
How many license plates exist with the format ABC-123, but do no repeat letters or numbers?
License Plates Starting With "A"
How many license plates exist with format ABC-123, that start with the letter "A"?
License Plates With More Options
How many license plates exist when the first 3 spots must be letters, and the last 3 spots can be either letters or numbers?
License Plates Ending In "888"
How many license plates exist with format ABC-123, but the 3 numbers must be "888"?
License Plates Without "I", "O", or "Q"
How many license plates exist with ABC-123 format, but the letters "I", "O", or "Q" cannot be used.
Passwords That Have 6 Letters And 1 Number
How many passwords exist that have exactly 6 letters and 1 number?
iPhone Lock Codes
How many 4-digit cell phone lock codes exist?
Combination Lock
How many possible combinations exist with a combination lock that has numbers 0-39?
Four-Direction Lock
How many possible combinations exist with a lock that has four directions.
Even 2-Digit Numbers Less Than 80
How many 2-digit numbers less than 80 are there?
Odd 3-Digit Numbers Greater Than 300
How many 3-digit number greater than 300 are there?
Sitting At a Movie Theatre
How many ways can 2 adults and 5 children sit in 7 consecutive seats, if an adult must sit at each end?
Families Sitting At A Movie Theatre
How many ways can 3 familes of 3 people each sit in 9 consecutive seats, if each family must sit together?
Ice Cream Store With Over 30,000 Combinations
If an ice cream store claims to have over 30,000 different topping combinations, how many toppings does it need to have?