There are 5 tasks and 5 persons. Task-l cannot be assigned to either person-l or person-2. Task-2 must
Answers
Given : There are 5 tasks and 5 persons. Task-l cannot be assigned to either person-l or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task
To Find : In how many ways can the assignment be done? (a) 6 (b) 12 (c) 24 (d) 144
Solution:
There are 5 tasks and 5 persons. Task-l cannot be assigned to either person-l 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? (a) 6 (b) 12 (c) 24 (d) 144
Task 1 can not be assigned to person-l or person-2
3 cases Task 1 can be assigned to person 3 , 4 or 5
Task 1 - person 3
Task-2 must be assigned to person-4
remaining 3 task to 3 person in 3! = 6 ways
Ways = 1 * 1 * 6 = 6
Task 1 - person 4
Task-2 must be assigned to person-3
remaining 3 task to 3 person in 3! = 6 ways
Ways = 1 * 1 * 6 = 6
Task 1 - person 5
Task-2 must be assigned to either person-3 or person-4 ( 2 ways)
remaining 3 task to 3 person in 3! = 6 ways
Ways = 1 * 2 * 6 = 12
Total Ways = 6 + 6 + 12 = 24
in 24 ways assignments can be done
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