# The special factorial inequality

Consider the inequality below,

$x! + y! + z! > (x + y + z)!$

For some ordered triplets $(x,y,z)$, the inequality holds. If $x,y,z$ ranges all over integer values from $0$ to $10$ inclusive, find the numbers of ordered triples that satisfy the inequality.

Details and assumptions

The values of $x,y,z$ are not necessarily distinct.

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