Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z.…
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
Solution
From the first seven natural numbers (1-7), the triplets satisfying x > 2y > 3z are (5,2,1), (6,2,1), (7,2,1) and (7,3,1). That is 4 distinct triplets.