SOLUTION: Please help me solve this problem. The topic is probability. A password consists of a letter chosen from 26 letters, three numbers between 0 and 9, and two characters consisting o

Question 1100863: Please help me solve this problem. The topic is probability.
A password consists of a letter chosen from 26 letters, three numbers between 0 and 9, and two characters consisting of ?,!,%,&,@. How many different combinations could you make?
Found 2 solutions by greenestamps, richwmiller:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

You don't mean combinations here. In a password, the order of the characters is important.

Assuming "between 0 and 9" means including 0 and 9, there are 10 choices for the digits.

Then we need to...
choose 1 of the 26 letters: C(26,1) = 26
choose 3 of the 10 digits: C(10,3) = 120
choose 2 of the 5 other characters: C(5,2) = 10

Then, since the statement of the problem did not prescribe any order for all the 6 characters of the password, they can be arranged in 6!=720 different orders.

Then the total number of possible passwords is

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On reading the problem again, there are several possible interpretations.

The solution above assumes that neither digits nor special characters can be repeated; and it assumes that there is no specified order for the total of 6 characters.

If digits or special characters can be used more than once, then the number of choices is greater; and the number of different arrangements now is complicated by the possibility of repeated characters.

And if there was some unstated condition about the order of the different types of characters, then the whole problem changes.

So the solution I showed my be not at all what you were looking for.

Resubmit the problem if necessary, making it absolutely clear what the requirements for the password are.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
This is at least the third time that this problem has been submitted which is fine as long as you wait 24 hours to resubmit. If you have clarification of the problem as greenestamps requested, you may resubmit right away.
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