QA – Placement Quizzes | Permutation and Combination | Question 11

Out of 6 engineers and 4 doctors, how many groups of 4 professionals can be formed such that at least 1 engineer is always there?
(A) 129
(B) 109
(C) 229
(D) 209


Answer: (D)

Explanation: There are four cases:

  1. 4 engineers = 6C4 = 15
  2. 3 engineers and 1 doctor = 6C3*4C1 = 20*4 = 80
  3. 2 engineers and 2 doctors = 6C2*4C2 = 15*6 = 90
  4. 1 engineer and 3 doctors = 6C1*4C3 = 24

Therefore, total number of ways = 15 + 80 + 90 + 24 = 209.

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