Question

Sydney’s security company uses security codes that are 2 letters followed by 3 numbers. How many different codes are possible if letters and numbers cannot be repeated?

Answer 1

468,000 different codes

Explanation:

The code has first 2 letters and then 3 numbers.

The first letter has 26 possibilities to be filled.

The second letter has 25 possibilities, as one letter is already used.

Then, for the numbers, we have:

The first number has 10 possibilities to be filled.

The second number has 9 possibilities to be filled (one used).

The third number has 8 possibilities to be filled (two used).

So, the total number of different codes is:

26*25*10*9*8 = 468,000 different codes.