Restricted Task Assignment

CAT 2006 Slot 1 · QA · Medium · Quantitative Aptitude

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There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

  1. A.

    144

  2. B.

    180

  3. C.

    192

  4. D.

    360

  5. E.

    716

Answer

144

Explanation

Task 2 can be assigned to person 3 or 4 (2 options, say person 3). Now person 3 is used. Task 1 cannot be assigned to person 1 or person 2. So Task 1 must be assigned to person 4, 5, or 6 (3 options). After assigning Task 2 and Task 1, 4 persons and 4 tasks remain, which can be assigned in 4!=244! = 24 ways. Total ways =2×3×24=144= 2 \times 3 \times 24 = 144.

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