Question

(To log on to a certain computer account, the user must type in a 3-letter password. In such apassword, no letter may be repeated, and only the lower case of a letter may be used. How manysuch 3-letter passwords are possible? (There are 26 letters in the alphabet.

Answer 1

The total number of possible password combination is 15,600 passwords

Here, we want to know the possible number of password combinations

The restrictions are that we are to use only lower case letters, and no repetition of letters is allowed

The number of letters to choose from are simply 26 lower case letters

The first letter has 26 to choose from

The second is from the remaining 25

The third letter has only 24 choices to select from

The total number of possible combinations is the product of this three

Mathematically, we have this as;

$26\times25\times24\text{ = 15,600}$