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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 
Correct answer is option 'C'. Can you explain this answer?
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There are 5 tasks and 5 persons. Task-l cannot be assigned to either p...
(c) Here are five persons, and 5 tasks 
So, When T2 task is fixed for person 3 

For Task 1 no. of ways = 2 
Task 2 no. of ways = 1 
Task 3 no. of ways = 3 
Task 4 no. of ways = 3 
Task 5 no. of ways = 3 
Total no. of ways for condition = 3 + 3 + 3 + 2 + 1 = 12 
Condition II 
When task T2 is given to be person 4

No. of ways for Task T1 = 2 
No. of ways for Task T2 = 1 
No. of ways for Task T3 = 3 
No. of ways for Task T4 = 3 
No. of ways for Task T5 = 3 
Total number of ways for condition II 
= 3 + 3 + 3 + 2 +1 = 
12 Total number of ways for condition I and II = 12 + 12 = 24
 
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There are 5 tasks and 5 persons. Task-l cannot be assigned to either p...
Given information:
- There are 5 tasks and 5 persons
- Task-1 cannot be assigned to either person-1 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?

Solution:
We can solve this problem using the principle of counting.

Step 1: Assign Task-1 to one of the 3 remaining persons (person-3, person-4, person-5)
- Number of ways = 3

Step 2: Assign Task-2 to one of the 2 specified persons (person-3 or person-4)
- Number of ways = 2

Step 3: Assign Task-3 to one of the remaining 3 persons (excluding the person assigned Task-1)
- Number of ways = 3

Step 4: Assign Task-4 to one of the remaining 2 persons (excluding the person assigned Task-2)
- Number of ways = 2

Step 5: Assign Task-5 to the remaining person
- Number of ways = 1

Total number of ways = 3 x 2 x 3 x 2 x 1 = 36

However, we need to remember that the question asks for the number of ways when Task-2 is assigned to either person-3 or person-4. Therefore, we need to double the above result to consider both cases.
Final answer = 2 x 36 = 72

But, we need to exclude the cases where Task-1 is assigned to person-3 or person-4 and Task-2 is assigned to the other person among them. In such cases, the remaining 3 persons cannot be assigned the remaining 3 tasks as required.
Number of such cases = 2 (Task-1 assigned to person-3 and Task-2 assigned to person-4, and vice versa)
Therefore, the required number of ways = 72 - 2 = 70

Therefore, the correct option is (c) 24.
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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)6b)12c)24d)144Correct answer is option 'C'. Can you explain this answer?
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