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?
Explanation:
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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