The special factorial inequality

Number Theory Level 3

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.