Let |X| denote the number of elements in a set X. Let S={1,2,3,4,5,6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A,B) such that 1 ≤ |B| < |A| equals.

Correct option is A. 422
A and B are Independent events
P(A)P(B)=P(A∩B) → a/6 × b/6 = c/6 → ab=6c
|A| = a, |B| = b, |A∩B| = c
(a,b,c) = (3,2,1) so ⁶C₁⁵C₂³C₁ = 180
(a,b,c) = (4,3,2) so ⁶C₂⁴C₂²C₁ = 180
(a,b,c) = (6,1,1) so ⁶C₁ = 6
(a,b,c) = (6,2,2) so ⁶C₂ = 15
(a,b,c) = (6,3,3) so ⁶C₃ = 20
(a,b,c) = (6,4,4) so ⁶C₄ = 15
(a,b,c) = (6,5,5) so ⁶C₅ = 6
Total = 180 + 180 + 6 + 15 + 20 + 15 + 6 = 422