CAT 2006QA Question 22

Forming a committeeEasy

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?

Answer & solution

Correct answer: 144

  • 144

  • B

    180

  • C

    192

  • D

    360

  • E

    716

Solution

Task 2 can be assigned in 2 ways (either to person 3 or 4).

Task 1 can then be assigned in 3 ways (persons 4 or 3, 5 and 6)

The remaining 4 tasks can be assigned to the remaining 4 persons in 4! = 24 ways

∴ The assignment can be done in 24 × 2 × 3 = 144 ways

Hence, option (a).

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CAT 2006 QA Q22: There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be a — Solution | TheCATExam