# combinatorics how many passwords are possible [closed]

A valid password is a 5 character string made up of letters (A,B, . . . , Z) and numbers (0, 1, . . . 9) such that at least one number and at least two letters are used. How many valid passwords are there?

-

## closed as off-topic by Weapon of Choice, studiosus, Ivo Terek, anorton, hardmathJul 21 at 3:19

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Weapon of Choice, studiosus, Ivo Terek, anorton, hardmath
If this question can be reworded to fit the rules in the help center, please edit the question.

It works better if you give us some idea of why you are interested in the problem, what you know about it, what you've tried, where you get stuck, and so on. –  Gerry Myerson Jan 29 '13 at 4:01

$(26C4*10C1+26C3*10C2+26C2*10C3)*5!$

-
quick question. does the 5! at the end represent the different ways of permuting the way the 5 characters can be arranged in a password? –  dotdotdot Jan 30 '13 at 9:08
Yes it does..... –  Abhra Abir Kundu Jan 30 '13 at 10:44

HINT:

• How many $5$-character strings are possible altogether?

• How many of them are invalid because they contain no digit?

• How many of them are invalid because they contain no letter? How many are invalid because they contain exactly one letter?

• Are there any that are invalid because they contain too few digits and too few letters?

Now put the answers together to get the result.

-

Hint.

A valid password can be of the following type.

1. 4 letters, 1 number.
2. 3 letters 2 numbers
3. 2 letters and 3 numbers.

So count number of possibilities of each type and sum them up.

It will be good if you write your (partial) solution.

-