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Question
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?
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Solution
Number of desk occupied by one couple = 1
Only (4 + 1) = 5 persons to be assigned.
∴ Number of ways of assigning these 5 persons = 5! × 2!
Total number of ways of assigning 6 persons = 6!
∴ Probability that a couple has adjacent desk = `(5! xx 2!)/(6!) = 1/3`
So, the probability that the married couple will have no-adjacent desks = `1 - 1/3 = 2/3`.
Hence, the required probability = `2/3`.
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