Q. 25.0( 2 Votes )

Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?

Answer :

Total new employees = 6

So, they can be arranged in 6! ways


n(S) = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720


Two adjacent desks for married couple can be selected in 5 ways i.e. (1, 2), (2, 3), (3, 4), (4, 5), (5, 6)


Married couple can be arranged in the two desks in 2! ways


Other four persons can be arranged in 4! ways


So, number of ways in which married couple occupy adjacent desks


= 5 × 2! × 4!


= 5 × 2 × 1 × 4 × 3 × 2 × 1


= 240


So, number of ways in which married couple occupy non – adjacent desks = 6! – 240


= (6 × 5 × 4 × 3 × 2 × 1) – 240


= 720 – 240


= 480 = n(E)






Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Match the following

Mathematics - Exemplar