Answer:
15 different passwords.
Step-by-step explanation:
Since I need to make a password of 4 letters from 6 given letters without repeating any letters, this can be done using combination.
Combination has to do with selection of some object from a pool of many objects.
Generally, if r objects are to be selected from a pool of n objects, this can be done in nCr number of ways where:
nCr = n!/(n-r)!r!
Applying the formula, if 4 letters are to be selected from 6 letters, this can be done in 6C4 ways
6C4 = 6!/(6-4)!4!
= 6!/2!4!
= 6×5×4!/2×4!
= 6×5/2
= 15ways
This shows that I can use 15 different passwords without repeating any letter
