Kritesh 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?
(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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