## Bike purchase

**Question:**

*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 $3 \times 4 \times 2 = 24$.

(Answer: 24)