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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