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Difficulty:
75%
(hard)
Question Stats:
54% (02:05) correct
46%
(01:58)
wrong
based on 213
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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 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
(1) 144
(2) 180
(3) 192
(4) 360
(5) 716
16 May 2017, 08:36
Kudos
Bookmarks
Kritesh
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
(1) 144
(2) 180
(3) 192
(4) 360
(5) 716
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.
16 May 2017, 13:21
Kudos
Bookmarks
Kritesh
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
(A) 144
(B) 180
(C) 192
(D) 360
(E) 716
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:
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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