Suppose you went to a bike shop to purchase a bike. A bike comes in 3 different colors (Red, Blue, and Green), 4 different styles (cruiser, sport, touring, and standard) and 2 different materials (steel and titanium). How many different customization options do you have if you decide to purchase a bike?
Soln. In order to finalize your bike customization, you will have to decide on a color, a style and a material. Since you have 3 different colors to choose from, you can select a color in 3 different ways. Similarly, you can select a style in 4 different ways. Finally, you can select a material in 2 different ways.
Now, from the multiplication theorem, total number of customization options you have is the product of
the number of choices in each step. So, the total number of ways is .