Math

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I form a 3-digit number at random from the digits 1-9. What is the probability that my number has no repeated digits? All three digits the same? Exactly one repeated digit?

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number of cases with no repeating digits
= 9x8x7 = 504
number of cases where digits repeat
= 9x9x9 = 729
so prob(no repeating digits) = 504/729 = 56/81

all 3 digits repeat, could be 111 , 222, .. 999
or 9 of them
prob = 9/729 = 1/81

I am not clear what you mean by "exactly one repeated digit"

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one digit is repeated twice

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