Question

A passcode can have 4 or 5 digits. Digits can be repeated and leading 0s are allowed. So, 1234 would be a 4 digit code that is different from 01234, which is a 5 digit code. How many different passcodes are possible?

Answer 1

Solution:

First, let's look at the four-digit passcode. There are total 10 possible digits that can form the passcode. These are:

0,1,2,3,4,5,6,7,8,9

The first place can be filled with one of the 10 possible digits, the second place can be filled with one of the 10 possible digits, the third place can be filled with one of the 10 possible digits and the fourth place can be filled with one of the 10 possible digits. Therefore, the different number of passcodes with four digits is:

10x10x10x10 =10000

Now let's look at the five-digit passcode. There are total 10 possible digits that can form the passcode. These are:

0,1,2,3,4,5,6,7,8,9

The first place can be filled with one of the 10 possible digits, the second place can be filled with one of the 10 possible digits, the third place can be filled with one of the 10 possible digits, the fourth-place can be filled with one of the 10 possible digits. and the fifth place can be filled with one of the 10 possible digits. Therefore, the different number of passcodes with five digits is:

10x10x10x10 x10 =100000

Therefore, the total number of different passcodes that are possible is:

10000+100000 = 110000