# 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.