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a man enter a lucky draw that requires him to

A man enter a lucky draw that requires him to pick five different integers from 1 through 30 inclusive .he chooses his five number in such a way that the sum of their log base 10 is an integer.it turns out that the winning five number have the same property i.e., the sum of their log to base 10 is also an integer.What is the probability that he holds the winning number?

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