Assign employees

gibran · Posted: Thu May 15, 2008 7:28 am Post subject: Assign 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. 5
B. 6
C. 7
D. 8
E. 9

punit.kaur.mba · Posted: Thu May 15, 2008 7:41 am Post subject:

Either the 2question is incorrectly framed and should also consider the possibility that none of the employess are assigned to any office. That way the answer would be 5.

Else the answer should be 4 and i dont see that in the options!!

the 2 offices

Off 1, Off 2

No. of ways-

Off 1 - 3 , Off2 0
off1 - 2 , Off2 - 1
Off1 - 0, Off2 -3
Off1 - 1, Off2 - 2

Someone correct me if I m wrong!

aatech · Posted: Thu May 15, 2008 8:11 am Post subject:

IMO D

Case 1 - One office has all 3 employees and second has none - this can happen in 2 ways

Case 2 - One office has 1 employee and another office has 2 - this can happen in 6 ways

So total 8

Magellan · Posted: Thu May 15, 2008 8:27 am Post subject:

netigen · Posted: Thu May 15, 2008 11:38 am Post subject:

0 | 3 -> 1 way to do this
1 | 2 -> 3 ways to do this
2 | 1 -> 3 ways to do this
3 | 0 -> 1 way to do this
-------------
Total = 8 (assuming each employee is a unique individual 8))

punit.kaur.mba · Posted: Thu May 15, 2008 11:54 am Post subject:

Actually aatech is right. The answer is 8.

We are right in selecting cases but wrong in counting the number of arrangements in that case.

In second case

(2,1) and (1,2)

Each case inturn has 3 ways becos we are "arranging" people between 2 offices here.

So if E denotes Employee and O denotes office

Selecting E1 and E2 is not same as selecting E2 and E3.

So within the second case

1) 3 ways of arranging people in O1,O2
(a) O1 - E1 and O2-E2,E3
(b)O1-E2 and O2-E1,E3
(c)O1-E3 and O2-E1,E2

2) similar to above case but just reversed

(a) O1 - E2,E3, O2 - E1
(b) O1- E1,E3 O2-E2
(c)O1-E1,E2 O2- E3

Magellan · Posted: Thu May 15, 2008 12:11 pm Post subject:

OK, I see. Difference between permutation and combination if I am not mistaken.

ektamatta · Posted: Thu May 15, 2008 6:33 pm Post subject:

there is another way to solve this problem

2 office
3 employees

2^3

8 ways

lunarpower · Posted: Fri May 16, 2008 10:38 pm Post subject:

umaa · Posted: Wed Jun 25, 2008 4:27 am Post subject: easy way

An easy way to find it. You have an equation to find this if there are no conditions. That is, n^r. which is 2^3=8.