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anonymous

  • 5 years ago

How many license plates can you build with 3 letters and 3 numbers with repetitions? You also need the additive principle.

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  1. anonymous
    • 5 years ago
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    26*26*26*10*10*10 26 possible letters, 10 possible numbers. You can start with 26 different letters. For each, the next can be 26 different letters. For each of those, 26 possible letters. Then, for each of those, 10 possible numbers and so on

  2. anonymous
    • 5 years ago
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    26*26*26*10*10*10 26 possible letters, 10 possible numbers. You can start with 26 different letters. For each, the next can be 26 different letters. For each of those, 26 possible letters. Then, for each of those, 10 possible numbers and so on

  3. anonymous
    • 5 years ago
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    that cant be right because there are only 3 letters and 3 numbers

  4. anonymous
    • 5 years ago
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    then you need to calculate possible ordering and remove new orders that duplicate. Try it and post if you get stuck

  5. anonymous
    • 5 years ago
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    where is the 26 and 10 coming from

  6. anonymous
    • 5 years ago
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    26 letters in the alphabet, 10 different digits

  7. anonymous
    • 5 years ago
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    you can only use 3 letters and 3 numbers

  8. anonymous
    • 5 years ago
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    it doesnt say 26 numbers

  9. anonymous
    • 5 years ago
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    26 letters

  10. anonymous
    • 5 years ago
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    I think that means 3 of the characters on the plates are letters, and there are 26 different choices for each letter slot. Maybe I'm misunderstanding, but that is what the question would normally ask

  11. anonymous
    • 5 years ago
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    How many license plates can you build with 3 letters and three numbers with repetiion

  12. anonymous
    • 5 years ago
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    so im thinkink its sayying like letters {a,b,c} and numbers {1,2,3}

  13. anonymous
    • 5 years ago
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    so MKV123 is 3 of each, but so is JHC567. Both are 3 of each, as is 1T2U4B

  14. anonymous
    • 5 years ago
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    no

  15. anonymous
    • 5 years ago
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    the 26*26*26 thing was right

  16. anonymous
    • 5 years ago
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    but i have to use the additive princible

  17. anonymous
    • 5 years ago
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    yeah, because you can start with a letter or a number which increases the permutations, then reduce that for the reorderings that end up duplicating a permutation

  18. anonymous
    • 5 years ago
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    can you show me how to do it im not understanding what to do

  19. anonymous
    • 5 years ago
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    so in your book, you have stuff like 3P26, 10C12 and that sort of thing. the 26 P 3 rather... 26 things taken 3 at a time. There will be a formula with it

  20. anonymous
    • 5 years ago
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    but we can have repeats, so we are really using 26 P 1 three times

  21. anonymous
    • 5 years ago
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    which gives us the 26*26*26

  22. anonymous
    • 5 years ago
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    yeah i figured that out im not sure where to go from there

  23. anonymous
    • 5 years ago
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    so you do 26*26*26*10*10*10 first. Then we can start with any of the three letters or numbers, yes? So 6 choices, then 5 for the next slot, 4 choices for the third slot and so on, and that ends up being 6! which we multiply our already big number by

  24. anonymous
    • 5 years ago
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    We would be done here except that we don't want to double count duplicates. if I have WWC567 and I swap the two Ws, then I don't actually have a new license number

  25. anonymous
    • 5 years ago
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    So we need to figure out how many times that happens

  26. anonymous
    • 5 years ago
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    For any given arrangement, only swapping around letters or numbers with the same type could duplicate us. If I swap a letter and a number, I'm going to have a new arrangement.

  27. anonymous
    • 5 years ago
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    Is there anyone else that can jump in here? I need to run. I didn't think this would take a while.

  28. anonymous
    • 5 years ago
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    This bit is where you use the combinations formulas to eliminate repeats

  29. anonymous
    • 5 years ago
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    I'm sorry, I have to meet friends in 10 minutes. Reread the examples in your book and see how far you get. Hopefully someone else will jump in!

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