Skip to content
Related Articles

Related Articles

Improve Article

GATE | GATE-CS-2006 | Question 25

  • Last Updated : 14 Feb, 2018
Geek Week

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 X_j that contain the element i. That is, f(i) = |{j|i \epsilon X_j}|.
Then, \sum_{i=1}f(i) is :
(A) 3m
(B) 3n
(C) 2m + 1
(D) 2n + 1

Answer: (B)

Explanation: First of all, number of subsets of S of size 3 is mC3 i.e. n=mC3. Now we count number of subsets in which a particular element i appears, that will be (m−1)C2, because 1 element is already known, and we have to choose 2 elements from remaining m-1 elements.

\sum\limits_{i=1}^{m} f(i) = m * ^{m-1}\mathrm{C}_2 = 3 * ^m\mathrm{C}_3 = 3n

Quiz of this Question

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up
Recommended Articles
Page :