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There are $6$ tasks and $6$ persons. Task $1$ cannot be assigned either to person $1$ or to person $2.$ Task $2$ must be assigned either to person $3$ or person $4.$ Every person is to be assigned one task. In how many ways can the task assignment be done?

  1. $144$
  2. $180$
  3. $192$
  4. $360$
  5. $716$
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Here we have restriction on 1st and 2nd task. 

For 2nd task we have only 2 choices.

For 1st task we have total            - 4 choices, { ecxept 1 and {3 or 4} }

For 3rd task we will have total     - 4 choices. { except who are assigned to task 1 and 2}

Similaly, for 4th task                     - 3 choices.

                for 5th task                     - 2 choices.

               for 6th task                      - 1 choices.

So total possibilities of task assignment = 4 * 2 * 4 * 3 * 2 * 1 = 192.

Ans. - 3.

 

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Task 2 can be assigned in 2 ways (either to person 3 or person 4).

Given that Task 1 cannot be assigned either to person 1 or to person 2.


So,Task 1 can then be assigned in 3 ways (persons 3 or 4, 5 and 6)

Number of ways to assign remaining 4 tasks to 4 persons = 4 ! = 24 ways

The assignment can be done in 24 × 2 × 3 = 144 ways

Hence, option (1)144 is the correct choice.

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