There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to 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?
(a) 144 (b) 180 (c) 192 (d) 360 (e) None of these
(a) Task 1 can not be assigned to either person 1 or 2 i.e.
there are 4 options.
Task 2 can be assigned to 3 or 4
So, there are only 2 options for task 2.
So required no. of ways = 2 options for task 2 × 3
options for task 1 × 4 options for task 3 × 3 options for
task 4 × 2 options for task 5 × 1 option for task 6.
= 2 × 3 × 4 × 3 × 2 × 1 = 144