Fundamental Counting Principle

Question 1

What is the fundamental counting principle?

Answer 1

If a task involves several stages in which there are 4 ways to do stage 1, 2 ways to do stage 2 and 6 ways to do stage 3, the total number of ways to do the entire task is 4x2x6 = 48

Question 2

If a lock has a three digit code and each digit can be 0 to 9 (10 possibilities), how many different codes can be made?

Answer 2

10x10x10 = 1000 different codes can be made

Question 3

If you are making an outfit and you have 3 pairs of pants to choose from, 4 shirts and 2 scarves (assuming that you only wear one of each type), how many different outfits can you create?

Answer 3

3x4x2 = 24 different outfits

Question 4

If you are making a word with four letters and:

• the first letter must be a vowel (y doesn’t count as a vowel)
• the second letter must be b, c or f
• the third letter must be x, y or z
• the fourth letter must be t

How many different words can you make?

Answer 4

5x3x3x1 =45 different words

Question 5

If you are making a committee and you can choose:

• either Sarah or Betty for president
• either Matt, Chris or Evan for vice president
• Mary, Ursula or Ariel for secretary

How many different committees can you make?

Answer 5

2x3x3 = 18