A committee of 4 members must be formed by selecting 2 engineers from a pool of 3 engineers (E1, E2, E3) and 2 accountants from a pool of 4 accountants (A1, A2, A3, A4). If Engineer E1 and Accountant A2 cannot serve on the same committee, how many different valid committees can be formed?

Answer and explanation

Correct answer: D. 12 committees

  1. Step 1: Total unconstrained committees: Choose 2 engineers from 3: C(3,2) = 3. Choose 2 accountants from 4: C(4,2) = 6. Total = 3 6 = 18. Step 2. Committees containing BOTH E1 and A2: To complete the team, choose 1 more engineer from {E2, E3} (2 choices) and 1 more accountant from {A1, A3, A4} (3 choices). Incompatible committees = 2 3 = 6. Step 3. Valid committees = 18 - 6 = 12. Answer: 12 committees, subtracting the 6 incompatible combinations from the 18 total combinations. Why not the others: 18 ignores the restriction; 15 subtracts only 3.

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