Multiplication Principle

Definition Of Multiplication Principle:

Multiplication Principle states: If an event occurs in m ways and another event occurs independently in n ways, then the two events can occur in m × n ways.

Examples of Multiplication Principle:

A pizza corner sells pizza in 3 sizes with 3 different toppings. If Bob wants to pick one pizza with one topping, there is a possibility of 9 combinations as the total number of outcomes is equal to Number of sizes of pizza × Number of different toppings.

Solved Example on Multiplication Principle

Ques: Brad is throwing a party. He is planning to serve Sandwiches and Ice creams to his guests. He has ordered four different types of Sandwiches: Hamburger (H), Grilled Sandwich (GS), Boiled Sandwich (BS) and Pressed Sandwich (PS), and two different flavors of Ice creams: Chocolate(C) and Strawberry (S). Find the number of possible combinations of a Sandwich and an Ice cream that Brad can serve to each of his guests.

Choices:

A. 8
B. 6
C. 16
D. 9
Correct Answer: A

Solution:

Step 1: The total number of outcomes = Number of possibilities of sandwich × Number of possibilities of ice cream 
Step 2: = 4 × 2 = 8 [As there are four different types of sandwiches and two different flavors of ice cream.]
Step 3: So, Brad can serve to each of his guests a Sandwich and an Ice cream in 8 different combinations.