6 employees, 2 of them are married to each other, are to be assigned desks that are lined up in a row. if the desks are chosen at random, what is the probability that the married couple will have non adjacent desks?

Dear student,

First we need to find the probability of the married couple getting adjacent seats, and then subtract it from 1.
let A,B,C,D,E,F are 6 employees and let A and B are couple.Now number of ways to arrange 6 people keeping AB side by side=Number of ways to arrange [AB],C,D,E,F +Number of ways to arrange [BA],C,D,E,FThereforeNow number of ways to arrange 6 people keeping AB side by side=5!+5!=120+120=240Now the number of ways to arrange 6 people will be my total sample size=6!=720Hence probability that couple will have adjacent desk=240720P(r)=13The probability that couple will have non adjacent desk.1-P(r)=1-13Answer=23

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