Multiplication Principle and Outcomes Worksheet

A diner menu offers 3 appetizers, 5 main courses, and 2 desserts. How many different three-course meals can a customer choose?

30 meals (3 x 5 x 2 = 30)

A bicycle lock requires a 4-digit code using digits 0 through 9. How many codes are possible if digits can be repeated?

10,000 codes (10 x 10 x 10 x 10 = 10,000)

How many 4-digit codes can be formed using digits 0 through 9 if no digit may be used more than once?

5,040 codes (10 x 9 x 8 x 7 = 5,040)

In how many different ways can 6 runners finish in 1st, 2nd, and 3rd place with no ties?

120 ways (6 x 5 x 4 = 120)

Four students line up single file for lunch. How many distinct line arrangements are possible?

24 arrangements (4 x 3 x 2 x 1 = 24)

A quiz has 5 true-or-false questions. How many unique ways can the answer key be completed?

32 ways (2 x 2 x 2 x 2 x 2 = 32)

A car model comes in 6 exterior colors, 2 interior colors, and 3 trim styles. What is the probability that a randomly assembled car has a red exterior, black interior, and sport trim?

1/36 (Total outcomes = 6 x 2 x 3 = 36; favorable = 1; probability = 1/36)

A club of 8 members elects a president, vice president, and treasurer. No member can hold two positions. What is the probability that Alex is president, Sam is vice president, and Taylor is treasurer?

1/336 (Total outcomes = 8 x 7 x 6 = 336; favorable = 1; probability = 1/336)