a computer password contains three different letters of the alphabet followed by two different digits from 0 to 9 how many different passwords are possible

You can work this out for yourself.

You have said three different letters of the alphabet followed by four different digits. I’m going to be lazy, and assume you don’t actually mean they have to be different. I’m also going to ignore capitals, because you didn’t specify these - but you can easily add them later by using 52 instead of 26 in step 4(a).

Let’s start with the back end first, because it is easier to understand and helps explain the front end.

What is the largest possible number you can express with four digits?

We have ten digits to choose from, and four places in which to put them.

10^4 is 10,000, but you can’t quite get there - you can only get to 9,999.

This means that the maximum possible permutations of part two of the password is 9,999.

Now to the first part.

Three letters, from a 26 letter alphabet? Same methodology as in 3(b).

26^3–1 is 17,575. Your password’s first three characters can form any of this many combinations.

Finally, we put them together. Oops - you made it way too easy. You didn’t mix letters and numbers, you just specified 3 letters and four digits.

So you have the total number of letter combinations and the total number of digit combinations. Multiply these together, and that is your (all-too-easily crackable by a simple computer program) answer.

Step-by-step explanation:

Number of ways of selecting 3 different letters and then arranging them is  26C1×25C1×24C1×3!=26×25×24×6=93600  

Number of ways of selecting 4 different digits from 0 to 9 and then arranging them is  10C1×9C1×8C1×7C1×4!=10×9×8×7×24=120960  

Hence total number of ways is  93600×120960=1132185600  ways