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anonymous

  • one year ago

How many seven-digit numbers can be formed from the digits 0-9 if each digit can be used more than once?

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  1. anonymous
    • one year ago
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    |dw:1439939273412:dw|

  2. anonymous
    • one year ago
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    I dont know if that is right or not?

  3. jchick
    • one year ago
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    This depends on whether the digits of the number can be repeated.... is 1123456 allowed, or do the digits all have to be different. Another question is can there be a leading 0 (or string of 0s, if duplication is allowed) So, working through the options, if no duplication is allowed, and the leading character cannot be 0, then there are 9 choices when we pick the first digit, 9 when we pick the second, 8 when we pick the third, 7 for the 4th, 6 for the 5th, 5 for the 6th and 4 for the 7th. 9 x 9 x 8 x 7 x 6 x 5 x 4 = 544,320 If we can lead with a 0 then there are 10 ways to pick the first digit, then 9 for the second, and so on down to 4 for the 7th. 10 x 9 x 8 x 7 x 6 x 5 x 4 = 604,800 If the digits can be repeated, but we cannot start with leading 0s then there are 9 ways to pick the first, and then 10 for each of the other positions 9 x 10 x 10 x 10 x 10 x 10 x 10 = 9,000,000 If we can use a leading 0 then we can choose from 10 digits for all positions and that is 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000

  4. jim_thompson5910
    • one year ago
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    JosephDeng your drawing would be correct if repeats weren't allowed

  5. anonymous
    • one year ago
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    |dw:1439939494880:dw| is that correct?

  6. jim_thompson5910
    • one year ago
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    since repeated digits are allowed, you compute 10^7 the long way to do it is to multiply out 10*10*10*10*10*10*10

  7. jim_thompson5910
    • one year ago
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    Smaller example: imagine instead of a 7 digit number, we form a 2 digit number (using 0 through 9, repeats allowed) set up a table with 10 rows and 10 columns. Along the top row we have 0 through 9. Along the left side we have 0 through 9. There will be 10*10 = 100 cells in the table that represent 00 through 99, which is exactly 100 different numbers

  8. anonymous
    • one year ago
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    so what would you use: permutation or combination?

  9. anonymous
    • one year ago
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    i get it now, but I want to know how to use the equation to solve

  10. jim_thompson5910
    • one year ago
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    you use neither because repeated digits are allowed

  11. jim_thompson5910
    • one year ago
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    permutation and combination both have the condition that repeats aren't used

  12. anonymous
    • one year ago
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    ah ok

  13. jim_thompson5910
    • one year ago
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    instead you'll use n^k where n is the number of choices per slot, and k is the number of slots

  14. jim_thompson5910
    • one year ago
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    n = 10 choices per slot (0 through 9) k = 7 slots because we're forming 7 digit numbers

  15. anonymous
    • one year ago
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    wait why -1?

  16. anonymous
    • one year ago
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    reading the number from left to right, example 4293855 the first digit can be 1-9 , so there are 9 choices the second digit can be 0-9 so there are 10 choices the third digit can be 0-9 so there are 10 choices the fourth digit can be 0-9 so there are 10 choices ... the seventh digit can be 0-9 so there are 10 choices

  17. anonymous
    • one year ago
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    So i get 9 x 10 x 10 x 10 x 10 x 10 x 10

  18. jim_thompson5910
    • one year ago
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    Oh right, I wasn't thinking. The first digit can't be 0

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