To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible? (There are 26 letters in the alphabet.)
Question
To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible? (There are 26 letters in the alphabet.)
Solution
To solve this problem, we need to use the concept of permutations.
A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by:
P(n, r) = n! / (n-r)!
In this case, we have 26 letters and we want to arrange 4 of them. So, n = 26 and r = 4.
Therefore, the number of 4-letter passwords that can be created is:
P(26, 4) = 26! / (26-4)!
= 262524*23
= 358,800
So, there are 358,800 possible 4-letter passwords.
Similar Questions
A website requires users to set up an account that is password protected. If the password format is four letters followed by a single digit number, how many different passwords are possible?
A password must start with a letter, be at least 6 characters long, include a number, not include any whitespace, and include a special symbol. How many of the following passwords are valid?hello, goodbye, Maker1, dog!three, Oops_again, 1augh#3
Answer the questions below.(If necessary, consult a list of formulas.)(a) From the 13 albums released by a musician, the recording company wishes to release 10 in a boxed set. How many different boxed sets are possible?(b) To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible? (There are 26 letters in the alphabet.)
Suppose a company needs temporary passwords for the trial of a new payroll software. Each password will have two letters, followed by one digit, followed by one letter. The letter W will not be used. So, there are 25 letters and 10 digits that will be used. Assume that the letters can be repeated. How many passwords can be created using this format?
a password consists of 3 letters from a to f inclusive and 4 digits from 0 to 9 inclusive.each letter and digit can only be usd once.how many different password can be formed?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.