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math..probabilities

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After three tosses of a fair die, which is more likely to come up: three distinct digits (e.g. 1,2,3), or three digits with at least one repeat (e.g. 1,2,1)?

Distinct digits is more likely
At least one repeat is more likely
They are the same
Cannot determine

Explain

  • math..probabilities -

    the only combinations with 3 distinct digits is
    1 2 3 , 2 3 4 , 3 4 5 , and 4 5 6

    Each of those can be arranged in 6 ways, so there are only 24 cases with the numbers distinct

    the 3 dice can fall in 6^3 or 216 different ways, so in 192 of those ways, one or more digits would repeat.

    So what do you think?

  • math..probabilities -

    what about the 3 distinct digits of 124, 125, 126, 134, 135, 136, 145, 146, 156, 235, 236, 245, 246, 256, 346 & 356?

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