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 ?
Based on the given constraints, there will be two cases in which task 1 is either assigned to one among person 3 or 4 or to one among person 5 or 6
Case 1:
Assigning Task 1 to either Person 3 or 4.
No. of ways of assigning task 1 = 2 ways
No. of ways of assigning task 2 = 1 way
Remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.
Therefore, Total number of ways = 2 x 1 x 4! = 48
Case 2:
Assigning Task 2 to either Person 5 or 6.
No. of ways of assigning task 1 = 2 ways
No. of ways of assigning task 2 = 2 ways
Remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.
Therefore, Total number of ways = 2 x 2 x 4! = 96
Hence, total number of possible arrangements= 48 + 96 = 144
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