The product rule is the number of ways to carry out a combination of activities = the number of ways to carry out each activity multiplied together.

Example 1:

How many different ways are there to roll four six-sided dice?

Each dice has 6 different ways that it can land (1, 2, 3, 4, 5 & 6).

Total number of ways of rolling four dice = 6 x 6 x 6 x 6 = 1296

Example 2:

Three fair coins are tossed. List all the possible outcomes and find the probability of getting exactly two heads.

HHT TTH HTH THT HTT THH TTT HHH

3/8 of these possible outcomes have exactly two heads.

Example 3:

A pizza place has 6 different toppings and you pick 4 different toppings.

How many unique pizzas are available?

Total ways to pick 4 from 6 = 6 x 5 x 4 x 3 = 360

Duplicate ways to arrange 4 items = 4! = 4 x 3 x 2 x 1 = 24

Total ways / duplicate arrangements = 360 / 24 = 15 unique combinations of toppings

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