6 employees, 2 of them are married to each other, are to be assigned desks that are lined up in - Maths - Probability

Question

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?

Shruti Tyagi · Accepted Answer

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
Regards,

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?