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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, In how many ways can the assignment be done?

A.

6

B.

12

C.

24

D.

144

Answer with explanation

Answer: Option CExplanation

Task 2 must be assigned to P_{4} or P_{3} =2C_{1}

For task 1 only 2 persons i.e.., P_{3} or P_{4}and P_{5} = 2C_{1}

Task 3 only 3 person available =3C_{1}

For task 4 only 2 persons available =2C_{1}

For task 5 only 1 person left = 1

Therefore, total number of ways

= 2C_{1} x 2C_{1}x 3C_{1}x 2C_{1} x1 = 2x2x3x2x1 =24

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