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

This can be solved using permutations.

Look at it like this:

First letter of the password can be selected in 7 ways, then Second in 6 ways, then 3rd in 5 ways, then fourth in 4 ways.

Hence: 7*6*5*4 = 840

OR

Formula for permutations of r objects out of n

= nPr = n!/(n -r)! = 7!/3! = 7*6*5*4 = 840