How many numbers are there between $100$ and $1000$ such that every digit is either $2$ or $9$?

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How many numbers are there between $100$ and $1000$ such that every digit is either $2$ or $9$?



I couldn't understand what actually the question means. Does it talk about the numbers like $222$, $999$?




combinatorics permutations




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    Also $229$, $929$, and so on.
    – saulspatz
    Aug 7 at 16:12






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    So, all the numbers between $100$ and $1000$ have 3 digits, right? So what can the first digit be? What can the second and the third?
    – stuart stevenson
    Aug 7 at 16:12















up vote
0
down vote

favorite












How many numbers are there between $100$ and $1000$ such that every digit is either $2$ or $9$?



I couldn't understand what actually the question means. Does it talk about the numbers like $222$, $999$?




combinatorics permutations




share|cite|improve this question















  • 2




    Also $229$, $929$, and so on.
    – saulspatz
    Aug 7 at 16:12






  • 3




    So, all the numbers between $100$ and $1000$ have 3 digits, right? So what can the first digit be? What can the second and the third?
    – stuart stevenson
    Aug 7 at 16:12













up vote
0
down vote

favorite









up vote
0
down vote

favorite











How many numbers are there between $100$ and $1000$ such that every digit is either $2$ or $9$?



I couldn't understand what actually the question means. Does it talk about the numbers like $222$, $999$?




combinatorics permutations




share|cite|improve this question











How many numbers are there between $100$ and $1000$ such that every digit is either $2$ or $9$?



I couldn't understand what actually the question means. Does it talk about the numbers like $222$, $999$?





combinatorics permutations





share|cite|improve this question










share|cite|improve this question




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asked Aug 7 at 16:10









blue_eyed_...

3,19321136




3,19321136







  • 2




    Also $229$, $929$, and so on.
    – saulspatz
    Aug 7 at 16:12






  • 3




    So, all the numbers between $100$ and $1000$ have 3 digits, right? So what can the first digit be? What can the second and the third?
    – stuart stevenson
    Aug 7 at 16:12













  • 2




    Also $229$, $929$, and so on.
    – saulspatz
    Aug 7 at 16:12






  • 3




    So, all the numbers between $100$ and $1000$ have 3 digits, right? So what can the first digit be? What can the second and the third?
    – stuart stevenson
    Aug 7 at 16:12








2




2




Also $229$, $929$, and so on.
– saulspatz
Aug 7 at 16:12




Also $229$, $929$, and so on.
– saulspatz
Aug 7 at 16:12




3




3




So, all the numbers between $100$ and $1000$ have 3 digits, right? So what can the first digit be? What can the second and the third?
– stuart stevenson
Aug 7 at 16:12





So, all the numbers between $100$ and $1000$ have 3 digits, right? So what can the first digit be? What can the second and the third?
– stuart stevenson
Aug 7 at 16:12











1 Answer
1






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oldest

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up vote
6
down vote



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You have three digits. Each digit must be selected from the set $2,9$. You may select either of those two for each digit. So, the first digit has two choices. The second digit has two choices. The third digit has two choices. Each choice is independent of the previous choices. This allows you to apply the product principle.



There are $2cdot 2cdot 2=8$ such numbers:



222,
229,
292,
299,
922,
929,
992,
999






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    1 Answer
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    1 Answer
    1






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    active

    oldest

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    up vote
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    down vote



    accepted










    You have three digits. Each digit must be selected from the set $2,9$. You may select either of those two for each digit. So, the first digit has two choices. The second digit has two choices. The third digit has two choices. Each choice is independent of the previous choices. This allows you to apply the product principle.



    There are $2cdot 2cdot 2=8$ such numbers:



    222,
    229,
    292,
    299,
    922,
    929,
    992,
    999






    share|cite|improve this answer

























      up vote
      6
      down vote



      accepted










      You have three digits. Each digit must be selected from the set $2,9$. You may select either of those two for each digit. So, the first digit has two choices. The second digit has two choices. The third digit has two choices. Each choice is independent of the previous choices. This allows you to apply the product principle.



      There are $2cdot 2cdot 2=8$ such numbers:



      222,
      229,
      292,
      299,
      922,
      929,
      992,
      999






      share|cite|improve this answer























        up vote
        6
        down vote



        accepted







        up vote
        6
        down vote



        accepted






        You have three digits. Each digit must be selected from the set $2,9$. You may select either of those two for each digit. So, the first digit has two choices. The second digit has two choices. The third digit has two choices. Each choice is independent of the previous choices. This allows you to apply the product principle.



        There are $2cdot 2cdot 2=8$ such numbers:



        222,
        229,
        292,
        299,
        922,
        929,
        992,
        999






        share|cite|improve this answer













        You have three digits. Each digit must be selected from the set $2,9$. You may select either of those two for each digit. So, the first digit has two choices. The second digit has two choices. The third digit has two choices. Each choice is independent of the previous choices. This allows you to apply the product principle.



        There are $2cdot 2cdot 2=8$ such numbers:



        222,
        229,
        292,
        299,
        922,
        929,
        992,
        999







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Aug 7 at 16:12









        InterstellarProbe

        2,262518




        2,262518






















             

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