A problem on probability

Three numbers are chosen at random from the set { 0 , 1 , 2 , , 29 } \{0,1,2,\ldots,29\} without replacement. The probability that the sum of the numbers is 30 is?

Answer is in the form of a b ) \dfrac{a}{b}) . Where a a and b b are coprime positive integers, find a + b a+b .


The answer is 827.

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