Integral Solutions

\[abcde=1050\]

and a, b, c, d, e are positive integers. How many ordered tuples \((a, b, c, d, e)\) exist?

Extra Credit: How many unordered sets \({a, b, c, d, e}\) exist?

Extra Credit: How many ordered tuples \((a, b, c, d, e)\) exist such that a≠b≠c≠d≠e?

Unrelated Credit: Solve the Aunty's Teacups problem

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