In such problems where distinct objects have to be assigned or distributed across distinct places, think from the perspective of 'what' is being distributed and 'where' is it being distributed.
'What' is people and 'where' is office here!
The first person has two choices as there are two offices. So, is the case with the next person and same for the third person.
So, we are looking at 2*2*2 = 8
A way to remember the result and not confuse for this type of problem is (where)^what. In our case (office)^people = 2^3.
Some other examples:
1> If the question were to post 3 distinct letters (what )to 5 different letterboxes (where) our result will be 5^3.
(You cannot post letter boxes to letters)
2> If 4 different prizes (what) need to be awarded to 3 students (where)our result will be 3^4.
(You cannot distribute students to prizes)
Note: In all the above cases we are talking about distinct objects and distinct places.
Assign employees
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Let X, Y and Z be the 3 employees.A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
A. 4
B. 6
C. 7
D. 8
E. 9
Let A and B be the 2 offices.
Take the task of assigning the employees and break it into stages.
Stage 1: Assign employee X to an office
There two options (office A or office B), so we can complete stage 1 in 2 ways
Stage 2: Assign employee Y to an office
There two options (office A or office B), so we can complete stage 2 in 2 ways
Stage 3: Assign employee Z to an office
There two options (office A or office B), so we can complete stage 3 in 2 ways
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus assign all employees to offices) in (2)(2)(2) ways ([spoiler]= 8 ways[/spoiler])
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EASY
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MEDIUM
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DIFFICULT
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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
