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There are 6 tasks and 6 persons. . . . .

This topic has 1 expert reply and 1 member reply

There are 6 tasks and 6 persons. . . . .

Post Fri Nov 10, 2017 6:06 am
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 to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

(1) 144

(2) 180

(3) 192

(4) 360

(5) 716

The OA is A .

Experts, what is the formula that I should apply here?

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ErikaPrepScholar Master | Next Rank: 500 Posts
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Post Tue Nov 14, 2017 6:05 am
To add on to what regor60 said above - the reason we start by assigning task 2 is because it's the most restrictive step. It's challenging to start with task 1, for instance, because the assignments for task 2 limit the options for task 1. After assigning task 2, we move to task 1 because it's the second most restrictive step. The remaining tasks have no restrictions, so we can assign them in any order.

So we have

Task 2: 2 options (P3 or P4)
Task 1: 3 options (P3/P4 [depending on assignment of Task 2] or P5 or P6)
Task 3: 4 options (remaining four people)
Task 4: 3 options (remaining three people)
Task 5: 2 options (remaining two people)
Task 6: 1 option (remaining one person)

2*3*4*3*2*1 = 144

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regor60 Master | Next Rank: 500 Posts Default Avatar
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Post Fri Nov 10, 2017 6:48 am
Vincen wrote:
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 to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

(1) 144

(2) 180

(3) 192

(4) 360

(5) 716

The OA is A .
First assign task 2, pick either 3 or 4, doesn' t matter, so choose 3 to start. This leaves 5 people remaining.

Assign task 1. Can't be persons 1 or 2, or 3. So 3 choices.

Assign task 3. Since you've selected 2 people to cover tasks 1 and 2, 4 choices remain
Assign task 4. 3 people remain to be chosen, so 3 choices.

Assign task 5. 2 people remain to be chosen so 2 choices

Assign task 6. 1 person remains, so 1 choice

Multiplying the choices out: 3x1x4x3x2x1 = 72

Then, remember you could also have assigned person 4 to do task 2, so this doubles the choices = 2x72 = 144

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