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In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

Correct answer: A. 5/21

  • A. 5/21
  • B. 5/14
  • C. 9/14
  • D. 16/21

Explanation

There are C(10,5) = 252 ways to choose five people. For at least two couples, choose two couples in C(5,2) = 10 ways and one of the remaining 6 people, giving 10 x 6 = 60 ways; hence 60/252 = 5/21. The likely mistake is 5/14, which comes from miscounting the possible extra person.

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