QA – Placement Quizzes | Permutation and Combination | Question 5

In how many ways can an interview panel of 3 members be formed from 3 engineers, 2 psychologists and 3 managers if at least 1 engineer must be included?
(A) 30
(B) 15
(C) 46
(D) 45


Answer: (C)

Explanation: The interview panel of 3 members can be formed in 3 ways by selecting 1 engineer and 2 other professionals, 2 engineers and 1 other professionals and all 3 engineers.

  • 1 engineer out of 3 engineers and 2 other professionals out of 5 professionals can be selected as
    = 3C1 * 5C2 = 3 * 10 = 30 ways.
  • 2 engineers out of 3 engineers and 1 other professional out of 5 professionals can be selected as
    = 3C2 * 5C1 = 3 * 5 = 15 ways.
  • 3 engineers out of 3 engineers and 0 other professional out of 5 professionals can be selected as
    = 3C3 * 5C0 = 1 way.

Hence, total number of ways = 30 + 15 + 1 = 46 ways.

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