Question

how many different three letter passwords can be formed from the letters A,B,C,D,E,F, and G if no repetition of letters is allowed

Answer 1

There are 210 possible three-letter passwords

Explanation:

We have 7 different letters. One example of a valid 3-letter password would be CFB. This other password EDE is not allowed because the E is repeated.

We need to find all the possible forms to have 3 different ordered letters out of 7 options.

We can place any valid letter as the first one like BXX. It can be done in 7 ways since we have them all available. Now we can replace the first X with the second letter, but now B is used, so we only 6 have six letters to use. That gives us 7x6= 42 combinations. Finally, the second X can be chosen from the remaining 5 letters. The answer is then

There are 7x6x5=210 possible three-letter different passwords