Calc - Numbers (Continued)

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