Question

There are $6$ tasks and $6$ persons. Task 1 cannot be assigned either to person 1 or 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?

Accepted Answer

C. **Case 1:** Task 2 is assigned to Person 3 or Person 4 (2 options). Suppose Task 2 is assigned to Person 3. Task 1 can be assigned to Person 4, 5, or 6 (3 options). Subcase 1a: Task 1 is assigned to Person 4. Remaining 4 tasks to 4 persons in $4! = 24$ ways. Total $= 2 	imes 1 	imes 1 	imes 24 = 48$. Subcase 1b: Task 1 is assigned to Person 5 or 6 (2 options). Remaining 4 tasks in $4! = 24$ ways. Total $= 2 	imes 2 	imes 24 = 96$. Total arrangements $= 48 + 96 = 144$.

Task assignment problem

Explanation

Practise this under exam conditions