Question 12

# There are 6 tasks and 6 persons. Task 1 cannot be assigned either to 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. In how many ways can the assignment be done ?

Solution

Based on the given constraints, there will be two cases in which task 1 is either assigned to one among person 3 or 4 or to one among person 5 or 6

Case 1:

Assigning Task 1 to either Person 3 or 4.

No. of ways of assigning task 1 = 2 ways

No. of ways of assigning task 2 = 1 way

Remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.

Therefore, Total number of ways = 2 x 1 x 4! = 48

Case 2:

Assigning Task 2 to either Person 5 or 6.

No. of ways of assigning task 1 = 2 ways

No. of ways of assigning task 2 = 2 ways

Remaining 4 tasks can be assigned among the remaining 4 persons in 4! ways.

Therefore, Total number of ways = 2 x 2 x 4! = 96

Hence, total number of possible arrangements= 48 + 96 = 144

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