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 ?

Correct Answer: (D) 24

Task-2 must be assigned to either R or S (2 choices). In Case 1, assign Task-2 to R. The remaining tasks are Task-1, Task-3, Task-4, Task-5, and remaining persons are P, Q, S, T. Since neither P nor Q can take Task-1, Task-1 must be assigned to either S or T (2 choices). The remaining 3 tasks can then be assigned to the remaining 3 persons in $3! = 6$ ways, giving $2$$\times$ 6 = 12 ways. In Case 2, assign Task-2 to S. Similarly, Task-1 must be assigned to R or T (2 choices), and the remaining 3 tasks assigned to 3 persons in $3! = 6$ ways, giving $2$$\times$ 6 = 12 ways. Total assignments $= 12 + 12 = 24$.