There are five persons P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done ?

• Task-2 must be assigned to either R or S, giving 2 possible choices for Task-2.

• Once Task-2 is assigned, 4 persons remain for the remaining 4 tasks (Task-1, Task-3, Task-4, Task-5).

• Task-1 cannot be assigned to P or Q. Since R or S is already taken for Task-2, the available persons for Task-1 are the two from {P, Q} who are not restricted? No, P and Q are restricted from Task-1. The remaining persons are P, Q, and the one from {R, S} not assigned to Task-2.

• Let's re-evaluate: If R takes Task-2, remaining are P, Q, S, T. Task-1 cannot be P or Q. So Task-1 must be S or T (2 choices).

• If S takes Task-2, remaining are P, Q, R, T. Task-1 cannot be P or Q. So Task-1 must be R or T (2 choices).

• In both cases, there are 2 valid choices for Task-1.

• After assigning Task-2 and Task-1, 2 persons remain for the last 2 tasks (Task-3 and Task-4), which can be arranged in 2! = 2 ways.

• Total ways = (2 choices for Task-2) * (2 choices for Task-1) * (2 ways for remaining tasks) = 8? Wait, let me re-read carefully.

• Let's list: Persons P, Q, R, S, T. Tasks 1, 2, 3, 4, 5.

• Constraint 1: Task 2 is R or S. (2 options)

• Case 1: Task 2 = R. Remaining persons: P, Q, S, T. Remaining tasks: 1, 3, 4, 5.

• Task 1 cannot be P or Q. So Task 1 must be S or T. (2 options)

• If Task 1 = S, remaining persons P, Q, T for tasks 3, 4, 5. Permutations = 3! = 6.

• If Task 1 = T, remaining persons P, Q, S for tasks 3, 4, 5. Permutations = 3! = 6.

• Total for Case 1 = 6 + 6 = 12.

• Case 2: Task 2 = S. Remaining persons: P, Q, R, T. Remaining tasks: 1, 3, 4, 5.

• Task 1 cannot be P or Q. So Task 1 must be R or T. (2 options)

• If Task 1 = R, remaining persons P, Q, T for tasks 3, 4, 5. Permutations = 3! = 6.

• If Task 1 = T, remaining persons P, Q, R for tasks 3, 4, 5. Permutations = 3! = 6.

• Total for Case 2 = 6 + 6 = 12.

• Total ways = 12 + 12 = 24.