amy is choosing a 2-letter password from the letters a, b, c, d, e, and f. the password cannot have the same letter repeated in it. how many such passwords are possible?

Amy can choose from 60 possible passwords.

Solution:

Given that the two-letter password is from the letters A, B, C, D, E and F

Total number of letters = 6  

The password is a two digit letter and repetition of letters is not allowed.

Method 1:

\therefore The number of ways of obtaining an ordered subset of r elements from a set of n elements is given by

So, the total possible password = = =

On cancelling the in numerator and denominator we get,

Here we get, = 30  possible passwords

Method 2:

There are 6 possible choices for the first term of the password and 5 choices for the second term (i.e. leaving the selected letter of the term)

So,