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GATE 2017 EC – Question 9

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

  1. 56
  2. 52
  3. 48
  4. 44

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Correct answer: (A) 56

Explanation

There are $2^6 = 64$ subsets of the 6 people. The ones with no Indian are the subsets of the 3 Chinese, which number $2^3 = 8$. So $64 - 8 = 56$ subsets have at least one Indian.