# Probability question

1. Feb 3, 2008

1. The problem statement, all variables and given/known data
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????

2. Relevant equations

im confused as to whether its a combination or a premutation

3. The attempt at a solution
didnt have a clue how to do this

2. Feb 3, 2008

### Avodyne

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.)

Last edited: Feb 3, 2008
3. Feb 3, 2008

### kuahji

Whats best to solve stats problems is to think about the problems logically. Formulas sometimes lead ya 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

4. Feb 3, 2008

### tramtran111

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

5. Feb 3, 2008

### kuahji

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

6. Feb 14, 2008

### Shooting Star

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.

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.

7. Feb 14, 2008

### HallsofIvy

Staff Emeritus
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."

8. Feb 14, 2008

### Shooting Star

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.

9. Feb 15, 2008

### HallsofIvy

Staff Emeritus
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.

10. Feb 15, 2008

### Shooting Star

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.