# Question

• Feb 19th 2011, 03:38 AM
hasanpak123
Question
9. Consider all 9-digit integers made by using all the digits 1,2,…,9. Write each such number on a separate sheet and put all the resulting sheets in a box. What is the minimum number of sheets that you must extract from the box if you want to be certain that there are at least two numbers with the same digit in the first place among the chosen numbers?
A) 9! B) 8! C) 72 D) 10 E) 9

• Feb 19th 2011, 04:25 AM
CSM
Quote:

Originally Posted by hasanpak123
9. Consider all 9-digit integers made by using all the digits 1,2,…,9. Write each such number on a separate sheet and put all the resulting sheets in a box. What is the minimum number of sheets that you must extract from the box if you want to be certain that there are at least two numbers with the same digit in the first place among the chosen numbers?
A) 9! B) 8! C) 72 D) 10 E) 9

Well, if you can't grasp this sort of questions at all, just try simpler cases, like 3 digit numbers with only using 3 digits.
[What are the options? I read it as you HAVE to use all the digits. So our options are: 123 and 132, 213, 231, 312, 321, indeed we have (3*2*1)=6 options. ]Because we have only 3 different starting numbers, pulling out 4 sheets will ensure we'll get two sheets with the same starting number.

I think you can solve the question now.
Btw everything between "[" and "]" isn't even needed. :P
• Feb 19th 2011, 07:19 AM
CaptainBlack
Quote:

Originally Posted by hasanpak123
9. Consider all 9-digit integers made by using all the digits 1,2,…,9. Write each such number on a separate sheet and put all the resulting sheets in a box. What is the minimum number of sheets that you must extract from the box if you want to be certain that there are at least two numbers with the same digit in the first place among the chosen numbers?
A) 9! B) 8! C) 72 D) 10 E) 9