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…
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?
6
12
18
24
Solution
Task-2 can be assigned to R or S: 2 choices. After fixing Task-2, Task-1 must go to someone other than P, Q and the person on Task-2, leaving 2 candidates from {R, S, T}. The remaining 3 persons fill the remaining 3 tasks in $3! = 6$ ways. Total $= 2 \times 2 \times 6 = 24$.