There are six tasks and six persons. Task 1 cannot be assigned to either person 1 or 2, task 2 must be assigned to either person 3 or person 4. Every person has to be assigned a task. In how many ways can the assignment be done?

There are six tasks and six persons. Task 1 cannot be assigned to either person 1 or 2, task 2 must be assigned to either person 3 or person 4. Every person has to be assigned a task. In how many ways can the assignment be done? Correct Answer 144

There are six tasks and six persons.

Tasks be – T1, T2, T3, T4, T5, T6

Persons – P1, P2, P3, P4, P5, P6

Task 2 must be assigned to either person 3 or person 4, so T2 can be done in 2 ways.

Task 1 cannot be assigned to either person 1 or 2, so four persons are remaining, out of which T3 will be done by either P3 or P4, so T1 can be completed in 3 ways.

For T3, there are 4 people remaining, so we can complete it in 4 ways.

For T4, 3 people are remaining, so we can complete it in 3 ways.

For T5, 2 people are remaining, so we can complete it in 2 ways.

For T6, 2 people are remaining, so we can complete it in 1 ways.

So, the number of ways in which the assignment can be done = 2 × 3 × 4 × 3 × 2 × 1

= 144