Sets and Functions

Question 1

Let S = {1,2,3,....,m}, m > 3. Let x1, x2,....xn be the subsets of S each of size 3. Define a function f from S to the set of natural numbers as, f(i) is the number of sets of Xj that contain the element i. That is f(i) = |{j|i ∈ Xj|}|.

Then is

A
3m
B
3n
C
2m+1
D
2n+1
Engineering-MathematicsSets And FunctionsGATE 2006
Question 1 Explanation: 
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