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  1. #1
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    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


    I don't get this at all^^... please help
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  2. #2
    CSM
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    Quote Originally Posted by hasanpak123 View Post
    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


    I don't get this at all^^... please help
    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
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by hasanpak123 View Post
    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


    I don't get this at all^^... please help
    If you choose 9 sheets the first digits could be 1,2,3,4,5,6,7,8 and 9. Which are all different. Now what happens when you take one more?

    CB
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  4. #4
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    oh i get it now... The 'minimum number'... i was thinking how can 10 'ensure' that we get two same first digit numbers cuz we can have 2 of the same numbers.... but i get it now... Thanks a lot!
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