Question

How many 3-letter passwords can be formed from the letters A through Z if

a) all letters in the password must be different (i.e ARJ)

b) all letters in the password must be different and they are in alphabetical order (i.e. AJR)

c) there are no restrictions (i.e. ARR)

Answer 1

a) If all letters in the password is different, then we have to

choose 3 letters out of 26 letters to construct the

password. It can be done in ways. Also the three

letters can interchange between themselves in 3! ways.

So, total number of ways = 3! = 15600 ways. (Ans).

b) We can choose 3 letters out of 26 letters in ways.

Now the three letters can again interchange between

themselves in 3! = 6 ways, but out of 6 ways, only 1 will be

in alphabetical order. So, total number of ways =

= 2600. (Ans).

c) If there are no restrictions, then the 1st letter can be

chosen in 26 ways, the 2nd in 26 ways and the 3rd also in

26 ways. So, total number of ways = = 17576. (Ans).