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If you put all 720 permutations of the digits 1 through 6 in numerical order from least to greatest (ex. 123456, 123465 etc.) What would the 409 permutation be? How do I do it?

  • math -

    Each permutaion of five numbers, following the first, has 120 possibilities. Therefore there are 360 numbers begining with 1, 2, or 3, and you are looking for the 49th number beginning with 4.

    4! = 24 numbers will begin with each two-number combination. 361 through 384 will begin with 41. 385 through 408 will begin with 42. Therefore your number will be the first (smallest) number begining with 43.

    What would that be?
    431256

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