Problem Solving

A software program is designed to generate password codes using alphabet from A to J, how many 4-alphabet password codes can the program generate? (please note: the alphabets are not allowed to repeat itself.)

A software program is designed to generate password codes using alphabet from A to J, how many 4-alphabet password codes can the program generate? (please note: the alphabets are not allowed to repeat itself.)?


Answer: A to J there are 10 aplhabets.

Each password is 4 digits length.

Every time you create a password you should pick 4 different letters so that you avoid repetition.

10C4 = 10!/6! * 4! = 210

210 is the correct answer

May I know the IMO?

nh8404052006 wrote:A software program is designed to generate password codes using alphabet from A to J, how many 4-alphabet password codes can the program generate? (please note: the alphabets are not allowed to repeat itself.)

I think answer would be 10C4 * 4! = 5040.

What is OA?

OA : [spoiler]10P4 /10^4[/spoiler]
I am not sure the OA is correct or not.

nh8404052006 wrote:OA : [spoiler]10P4 /10^4[/spoiler]

well! If I follow this answer then it can be break down to (9*8*7)/10*10*10 = 0.504.

Isn't there something wrong with the answer stated above by you?

I think answer would be 10C4 * 4! = 5040.???


Can you explain how did u come to this conclusion?

kishore wrote:I think answer would be 10C4 * 4! = 5040.???


Can you explain how did u come to this conclusion?

Selecting 4 alphabets from 10 alphabets = 10C4.
Arranging selected 4 alphabets to created different passcodes = 4!
Total no of ways = 10C4 * 4!

Let me know if there is some thing wrong in the approach.
Thanks

This is a permutation problem.
I am so happy to see so many ways that this problem can be solved.
I solved it analytically.

There are 10 alphabets and 4 positions.
mark them as
1----2----3----4

1st position can be filled by any 10 alphabets. So 10 ways
2nd position can be filled by any 9 alphabets. So 9 ways
3d " " "" 8 alphabets . So 8 ways
4th position needs 7 ways.

So total ways is a product of all these = 5040 ways.

Agree 100% with some posters on 5040

10*9*8*7