Question 117
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?
Solution
Assign Task 2 first: 2 choices (Person 3 or 4).
Total ways to assign the remaining 5 tasks: 5! = 120.
Total without Task 1 restrictions: 2*120 = 240.
Subtract restricted cases for Task 1:
If Task 1 is given to Person 1: 2*1*4! = 48.
If Task 1 is given to Person 2: 2*1*4! = 48.
Final Result: 240 - 48 - 48 = 144.
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