Let S={1,2,3,……,m}, m>3. Let X1,X2,……Xn be 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 Xj that contains the element i. That is f(i)=|{j|iϵXj}|. Then m∑i=1f(i) is

Let S={1,2,3,……,m}, m>3. Let X1,X2,……Xn be subsets of S each o

1.	Let S={1,2,3,……,m}, m>3. Let X1,X2,……Xn be 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 Xj that contains the element i. That is f(i)=\|{j\|iϵXj}\|. Then m∑i=1f(i) is
Answer» Let $S = {1, 2, 3, \dots \dots, m}, m > 3$ . Let $X_{1}, X_{2}, \dots \dots X_{n}$ be 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 $X_{j}$ that contains the element $i$ . That is $f (i) = \| {j \| i ϵ X_{j}} \|$ . Then $m \sum i = 1 f (i)$ is