Given that, S = {1, 2, 3,........, m}, m >3
Total number of elements in S = m
Total number of subsets of size 3 each can be ^{m}c_{3.}
Now suppose take 1st element 1. Out of ^{m}c_{3 subsets} 1 wont be there in ^{(m-1)}c_{3 }subsets.
So 1 will be there in ^{m}c_{3 }- ^{(m-1)}c_{3 }= (m-1)⨉(m-2)/2 subsets.
Similiarly for all remaining elements 2,3,4,5....m, we have same number of subsets.
i.e. ^{m}c_{3 }- ^{(m-1)}c_{3 }= (m-1)⨉(m-2)/2
(from i=1 to m ) ∑f(i) = (from i=1 to m ) ∑(m-1)⨉(m-2)/2 = m⨉(m-1)⨉(m-2)/2
In Qs given that ^{m}c_{3 }= n (No of X subset) , therefore m ⨉ (m-1) ⨉ (m-2)/2 = 3n
The correct answer is,(B) 3n