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Six new employees, two of whom are marri...

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?

Text Solution

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Let the couple occupied adjacent desks consider those two as 1.
There are (4+1)i.e., 5 persons to be assigned.
`therefore"Number of ways of assigning these five person"=5!xx2!`
`"Total number of ways of assigning 6 persons"=6!`
`therefore"Probability that the couple has adjacent desk"=(5!xx2!)/(6!)=(2)/(6)=(1)/(3)`
`"Probility that the married couple will have non-adjacent desks "=1-(1)/(3)=(2)/(3)`
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