anonymous
  • anonymous
The 7 members of a chess club line up for a picture. Determine the probability that Jordan and Ryan are not beside each other.
Probability
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anonymous
  • anonymous
The 7 members of a chess club line up for a picture. Determine the probability that Jordan and Ryan are not beside each other.
Probability
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
is that 21
anonymous
  • anonymous
7C2
anonymous
  • anonymous
(7! - 2!*6!) /7!

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anonymous
  • anonymous
got it?
anonymous
  • anonymous
5040-2*720/5040
anonymous
  • anonymous
$$\frac{7!-2!6!}{7!}=1-\frac{2!6!}{7!}=1-\frac27=\frac57$$
anonymous
  • anonymous
thnx guys
queelius
  • queelius
Others have already mentioned the solution but I thought I would explain how you get it. The way I solved it was by first finding out the probability of them being next to each other. So, we have 7 places. If they're next to each other, we have the following cases: Let A be Jordan and B by Ryan. A B _ _ _ _ _ B A _ _ _ _ _ _ _ A B _ _ _ _ _ B A _ _ _ And so on. In total, we have 12 configurations of this. In each of the blank positions, we do a simple permutation of the remaining people, i.e., 5!. So, we have 12 * 5! ways of arranging them, which equals 2 * 6! ways. There are 7! ways in total, without the constraint. So, the probability they are next to each other is: 2 * 6! / 7! = 2 / 7 The probability that they are not next to each other is 1 - 2 / 7, then, which is 5 / 7.
anonymous
  • anonymous
thnx queelius

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