Suppose a car door lock has a five-button keypad. Each of the buttons includes two digits.

How many different five-button patters are possible??
(Hint: Each button can be used more than once.)

2 to the fifth power.

why is that?

To find the number of different five-button patterns possible, we need to consider several factors.

First, let's analyze each button on the keypad. Each button includes two digits, so there are two choices for each button.

Since there are five buttons on the keypad, and each button can be used more than once, we need to calculate the total number of combinations.

To do this, we can raise 2 (the number of choices for each button) to the power of 5 (the number of buttons on the keypad):

Number of patterns = 2^5 = 32

Therefore, there are 32 different five-button patterns possible on the car door lock.