A computer password consists of a letter followed by 3 or 4 numbers. Find the total number of passwords that can be created.

Question

The answer is $286000$. Please tell me how can one get this answer.

Answer 1

There are 26 letters in the alphabet (A-Z) and 10 numbers (0-9).

This question has two cases:

1) A letter followed by three numbers

To get the number of permutations here, you need to multiply the different values each of the characters can have: $26\cdot10\cdot10\cdot10=26,000$

2) A letter followed by four numbers

To do this, do something similar to the above. Note that you'll need to have an extra 10 for the number of values of the last digit. $26\cdot10\cdot10\cdot10\cdot10=260,000$

Now to get the total number of password possibilities, you need to add these two.

$$26,000+260,000=286,000$$

Answer 2

The answer is: Number of letters in the alphabet to the 3rd power + number of letters in the alphabet to the 4th power. And this is number of all variations.