M7MBA wrote:A certain company assigns 5 rooms to each of its 5 employees in the marketing department. Next month, Company plans to change these employees rooms in such a way that no employee get the same room. In how many ways company can assign rooms to these employees.
a) 5
b) 8
c) 44
d) 60
e) 120
The problem above is the same as the following:
If the correct ordering for five letters is ABCDE, how many ways can the letters be arranged so that no letter is in the correct position?
A DERANGEMENT is a permutation in which NO element is in the correct position.
Given n elements (where n>1):
Number of derangements = n! (1/2! - 1/3! + 1/4! + ... + ((-1)^n)/n!).
Given 5 letters A, B, C, D and E:
Total number of derangements = 5! (1/2! - 1/3! + 1/4! - 1/5!) = 60-20+5-1 = 44.
The correct answer is
C.
The problem above seems too complex for the GMAT.
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