Hello everyone...im feeling lost on this question. The answer is 2/3. But i don't know how they are getting it.(adsbygoogle = window.adsbygoogle || []).push({});

Six new employees, two of whom are married to eachother, 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? (Hint: First find the probability that the coup will have adjacent desks, and then subtract this number from 1.)

Well I think i figured out how many ways the 2 married couple will end up in adjacent desks by the following:

I let A, B, C, D, E, F stand for the 6 employee's, i'm going to assume A and B are the married couple.

So...

[number of ways to place 6 together keeping A and B side by side] = [Number of ways to arrange [A B] C D E F ] + [ number of ways to arrange [B A] C D E F] = 5! + 5! = 120 + 120 = 240 ways to arrange the 6 employee's keeping A and B together (the married couple).

Now i know the total number of ways to place the 6 people together wolud be 6! = 720. So the probability that the couple will have adjacent desks is:

P = N(E)/N(S) = 240/720 = 1/3;

1 - 1/3 = 2/3.

I seeemed to figure the problem out while typing this hah, oh well that works! I should do this more often.

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# Homework Help: Tricky probabiity question

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