Play with the numbers!

\[\large a + b + c + d + e = 120\]

Let \(a, b, c, d, e\) be positive integers which satisfy the equation above such that \(a \geq 1\), \(b \geq 2\), \(c \geq 3\), \(d \geq 4\) and \(e \geq 5\). Then find the number of possible ordered 5-tuples \((a,b,c,d,e)\).

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