The set A = {(x,y,z)|x,y,z are integers

Question

The set A = {(x,y,z)|x,y,z are integers, 1≤x≤y≤z≤4} has n elements, then n =

a.10

b.16

c.20

d.27

e.64

Answer 1

Brute force logic works fine here, since there are so few possible triplets:

4 options with x=y=1 + 3 options with x=1, y=2 + 2 options with x=1, y=3 + 1 option with x=1, y=4. By similar logic, x=2 gives 3+2+1 options, x=3 gives 2+1 options, and x=4 generates the 20th and final integer triplet.