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?
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? Correct Answer 144
Calculation:
Based on the given constraints, there will be two cases in which task 1 is either assigned to one among persons 3 or 4 or to one among persons 5 or 6.
Case 1:
Assign task 1 to either Person 3 or 4.
Number of ways of assigning task 1 = 2 ways
Number of ways of assigning task 2 = 1 way
The remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.
Total number of ways = 2 × 1 × 4! = 48
Case 2:
Assign task 2 to either Person 5 or 6.
Number of ways of assigning task 1 = 2 ways
Number of ways of assigning task 2 = 2 way
The remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.
Total number of ways = 2 × 2 × 4! = 96
Total number of possible arrangments is 48 + 96 = 144
∴ The total number of possible arrangments is 144.
