Three numbers $x$ , $y$ , $z$ are selected from the set of the first seven natural numbers such that $x > 2y > 3z$ . How many such distinct triplets $(x, y, z)$ are possible?

One triplet

Two triplets

Three triplets

Four triplets

Kepler. Discussing PYQs. Q.no. 49

Three numbers xxx , yyy , zzz are selected from the set of the first seven natural numbers such that x>2y>3zx > 2y > 3zx>2y>3z . How many such distinct triplets (x,y,z)(x, y, z)(x,y,z) are possible?