Password Combinations: 2 Alphabetic + 3 Digits

In summary, the conversation discusses the problem of creating passwords using two alphabetic letters and three digits without any repetition. The approach suggested is a combination of permutation and combination, as well as considering the possibilities of the letters and digits appearing in any order. The conversation also notes the importance of reading the problem carefully and considering all possible interpretations.

Homework Statement

Passwords are made up of 2 alphabetic letters and 3 digits from the digits 3,4,5,6,7. How many passwords are there with no letter or digit being repeated?

Homework Equations

im confused as to whether its a combination or a premutation

The Attempt at a Solution

didnt have a clue how to do this

How many ways are there to chose the first letter/digit of the password?

After that choice is made, how many ways are there to choose the second letter/digit?

Etc.

(I'm assuming that the letters and digits can appear in any order; the problem could be read as saying that a password is 2 letters followed by 3 digits.)

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Whats best to solve stats problems is to think about the problems logically. Formulas sometimes lead you astray. Also, as Avodyne stated the question is ambiguously worded. Can the numbers & letters be in any order, or is it specifically 2 letters then 3 numbers?

If there is no specific order, slot one will have 26+5 possible choices. Then if the letter or number can't be repeated... how many choices will you have for the second slot?

31*second slot*third slot...*fifth slot

i got the answer! you just simply multiply these number 26 . 25. 5.4.3 =39000

tramtran111 said:
i got the answer! you just simply multiply these number 26 . 25. 5.4.3 =39000

Its best not to solve the problems for people, but rather to give them hints & allow them to solve the problem.

Avodyne said:
(I'm assuming that the letters and digits can appear in any order; the problem could be read as saying that a password is 2 letters followed by 3 digits.)

Your two sentences above contradict each other. Why should the problem could be read as you say? Any letter or number can sit anywhere, which you said in the first sentence.

tramtran111 said:
i got the answer! you just simply multiply these number 26 . 25. 5.4.3 =39000

Passwords are made up of 2 alphabetic letters and 3 digits from the digits 3,4,5,6,7. How many passwords are there with no letter or digit being repeated?

Homework Equations

im confused as to whether its a combination or a premutation
A bit of both.

Select any two alphabets, which can be done in 26C2 ways.
Select any three numbers now out of the five given in the same way.

All these cases are mutually exclusive and exhaustive. So, now just permute the five different symbols.

Avodyne said:
(I'm assuming that the letters and digits can appear in any order; the problem could be read as saying that a password is 2 letters followed by 3 digits.)

Shooting Star said:
Your two sentences above contradict each other. Why should the problem could be read as you say? Any letter or number can sit anywhere, which you said in the first sentence.

I believe it would be clearer if he had included a word "but"

"I'm assuming that the letters and digits can appear in any order; but the problem could be read as saying that a password is 2 letters followed by 3 digits."

HallsofIvy said:
I believe it would be clearer if he had included a word "but"

"I'm assuming that the letters and digits can appear in any order; but the problem could be read as saying that a password is 2 letters followed by 3 digits."

Well, if I had faced this problem in an exam, in the form the OP has given it, I would have interpreted it as the letters and numbers occurring in any position, which is Avodyne's first interpretation. Nowhere it is implied that the first two are alphabets.

But yes, with a "but" in Avodyne's second statement, it would remove the contradiction with his first assertion.

I agree with you. But posters here don't always copy the problem correctly and having "alphabet first, then digits" is common enough that it would be reasonable to at least note it.

HallsofIvy said:
I agree with you. But posters here don't always copy the problem correctly and having "alphabet first, then digits" is common enough that it would be reasonable to at least note it.

That is a good thing you have pointed out. I hadn't taken into consideration the youth of the posters here. I'll keep it in mind. Thanks, HallsofIvy.

1. How many password combinations are possible with 2 alphabetic characters and 3 digits?

There are 260,000 possible combinations for a password with 2 alphabetic characters and 3 digits. This is calculated by taking the number of possible alphabetic characters (26) and multiplying it by the number of possible digits (10) raised to the power of the number of digits (3).

2. Are passwords with 2 alphabetic characters and 3 digits secure?

While there are a large number of possible combinations for this type of password, it may not be considered completely secure. Brute force attacks and dictionary attacks can still potentially crack these passwords. It is recommended to use a combination of letters, numbers, and special characters for a more secure password.

3. What are the advantages of using 2 alphabetic characters and 3 digits in a password?

One advantage of using 2 alphabetic characters and 3 digits in a password is that it can be easier to remember than a long string of random characters. It also adds an extra layer of complexity compared to a password with only letters or numbers.

4. Can I use the same password combination for multiple accounts?

It is not recommended to use the same password combination for multiple accounts. If one account is compromised, it can make it easier for hackers to access other accounts with the same password.

5. How often should I change my password with 2 alphabetic characters and 3 digits?

It is generally recommended to change your password every 3-6 months for added security. However, if you suspect that your password has been compromised, it is important to change it immediately.

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