Product of digits in an 11-digit integer

Martin is constructing an 11-digit positive integer. The digits he has to choose from are \(1,2,3,5\) and \(7\) only. His number can contain at most one 1, at most two 2s, at most two 3s, at most four 5s, and at most eleven 7s. How many distinct possibilities are there for the products of the digits of the number that Martin is making?

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