Probability question

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

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:
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

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

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.

Shooting Star
Homework Helper
(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.

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.

HallsofIvy
Homework Helper
(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.

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."

Shooting Star
Homework Helper
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.

HallsofIvy