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 mc3.
Now suppose take 1st element 1. Out of mc3 subsets 1 wont be there in (m-1)c3 subsets.
So 1 will be there in mc3 - (m-1)c3 = (m-1)⨉(m-2)/2 subsets.
Similiarly for all remaining elements 2,3,4,5....m, we have same number of subsets.
i.e. mc3 - (m-1)c3 = (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 mc3 = n (No of X subset) , therefore m ⨉ (m-1) ⨉ (m-2)/2 = 3n
The correct answer is,(B) 3n