There are 6 tasks and 6 persons. Task 1 cannot be assigned either to

Question

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?

(A) 144

(B) 180

(C) 192

(D) 360

(E) 716

(1) 144

(2) 180

(3) 192

(4) 360

(5) 716

broall · Answer

There are 6 tasks T1, T2, T3, T4, T5, T6 
and 6 people P1, P2, P3, P4, P5, P6.

If T2 is assigned to P3 , there are 5 remaining tasks T1, T3, T4, T5, T6 and 5 remaining people P1, P2, P4, P5, P6.

T1 can't be assigned to P1 or P2, so T1 could be assigned to P4, P5, P6.
T3 could be assigned to each of 4 remaining people.
T4 could be assigned to each of 3 remaining people.
T5 could be assigned to each of 2 remaining people.
T6 could be assigned to the only remaining people.

Hence, the total combination in this case is 3*4*3*2*1.

If T2 is assigned to P4 . The result is the same as the first case above. The total combination is 3*4*3*2*1

Hence, the answer is 2*3*4*3*2*1=144

The answer is A.

BrentGMATPrepNow · Answer

Take the task of assigning the tasks and break it into   stages  .

Start with the  most restrictive stage(s) !

Stage 1 : Select a person to complete task 2 
Since task 2 must be assigned to either person 3 or person 4, we can complete stage 1 in  2  ways

Stage 2 : Select a person to complete task 1 
There are 5 people remaining who have not been assigned a task
However, task 1  cannot  be assigned to person 1 or to person 2
So, there are only 3 people to choose from. 
So we can complete stage 2 in  3  ways

Stage 3 : Select a person to complete task 3 
There are 4 people remaining, so we can complete stage 3 in  4  ways

Stage 4 : Select a person to complete task 4 
There are 3 people remaining, so we can complete stage 4 in  3  ways

Stage 5 : Select a person to complete task 5 
There are 2 people remaining, so we can complete stage 5 in  2  ways

Stage 6 : Select a person to complete task 6 
There is 1 person remaining, so we can complete stage 6 in  1  way

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus assign all 6 tasks) in  (2)(3)(4)(3)(2)(1)  ways (= 144 ways)

Answer:  A

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Kritesh · Answer

Let T1,T2,T3,T4,T5 &T6 be the Tasks and P1,P2,P3,P4,P5 & P6 be the Persons

Task T2 can be done only in 2 ways (either to P3 or P4)

Task T1 can be done in 3 ways (P5,P6, and 1 among P3/P4)

Task T3 can be done in 4 ways (Remaining 4 people)

Task T4 can be done in 3 ways (Remaining 3 people)

Task T5 can be done in 2 ways (Remaining 2 people)

Task T6 can be done in 1 way (Remaining 1 person)

So, totally there can be a combination of 2 * 3 * 4 * 3 * 2 * 1 ways = 144 Ways.

Hence option A is the answer

FillFM · Answer

Task 1 to person 3 > Task 2 to person 4:
1*1*4*3*2*1 = 24

Task 1 to person 4 > Task 2 to person 3:
1*1*4*3*2*1 = 24

Task 1 to person 5 or 6:
2*2*4*3*2*1 = 96

Total: 24+24+96 =  144

akadiyan · Answer

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?

(A) 144

(B) 180

(C) 192

(D) 360

(E) 716

Combination # 1:
T1 -> P3 , T2 -> p4 then T3 will have 4 options, T4 3 options, T5 - 2 options and T6 - 1 option
1*1*4*3*2*1 = 24

Combination # 2:
T1 -> P4 , T2->P3, then others will have same options as above
1*1*4*3*2*1 = 24

Combination # 3:
T1 is assigned to person 5 or person 6. 
T2 can be assigned to person 3 or person 4.
2*2*4*3*2*1 = 96

Adding all together = 24+24+96 = 144

Ans:  A

arpang · Answer

Watch this video for a 10 second solution to this question:

QCq6qRJCTj8

samarpan.g28 · Answer

6 tasks so T1, T2, T3, T4, T5 and T6.
6 person so P1, P2, P3, P4, P5 and P6.

Given, T2 can be done by either P3 or P4 i.e. 2 ways.
Also given, T1 can be done by T5, T6 and the remaining of P3 or P4 i.e. 3 ways.

Now calculate the other tasks: T3 - select 1 of the remaining 4 persons i.e. 4 ways. Similarly T4, T5 and T6 in 3, 2 and 1 ways.

Total: 2*3*4*3*2*1=144 ways. Option (A) is correct.

bumpbot · Answer

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