Eyas Posted May 1, 2009 Report Share Posted May 1, 2009 There are 10 seats in a row in a waiting room. There are six people in the room.(a) In how many different ways can they be seated?(b) In the group of six people, there are three sisters who must sit next to each other.In how many different ways can the group be seated? [6]Part A is easy and is solved with 10P6. But part B is the one I'm having a problem with.. our teacher never discussed permutations in class.For part B, the markscheme says this:Total number of ways = 8 x 3! x 7 x 6 x 5 = 10 080If someone can either explain the total number of ways when some elements are restricted/repeated that'd be great, or if someone can point me out to a good study guide/site that discusses this. Reply Link to post Share on other sites More sharing options...
moneyfaery Posted May 1, 2009 Report Share Posted May 1, 2009 For Part A, do you mean 10C6?For Part B, pretend there are 10 seats like so: _ _ _ _ _ _ _ _ _ _There are 8 ways for the 3 sisters (out of the 6 people) to sit together. It doesn't matter what order the sisters sit in so you use C and not P.S S S _ _ _ _ _ _ __ S S S _ _ _ _ _ __ _ S S S _ _ _ _ _ etcso 8 x 6C3 = 8 x 3!There are now 7 seats left which the 3 people can sit on in any order (order does matter).7P3 = 7! / 4! = 7 x 6 x 5Multiplying the two together gives 8 x 3! x 7 x 6 x 5 = 10 080 Reply Link to post Share on other sites More sharing options...
Eyas Posted May 2, 2009 Author Report Share Posted May 2, 2009 For part A its 10P6, since order is important as well.And thanks for the explanation for the the second part. It helped! Reply Link to post Share on other sites More sharing options...
moneyfaery Posted May 2, 2009 Report Share Posted May 2, 2009 Oh oops, now that I read the question again, that makes sense. :X Reply Link to post Share on other sites More sharing options...
Riptide Posted May 3, 2009 Report Share Posted May 3, 2009 Wouldn't 10P6 be for if there were 10 people trying to fill 6 seats? If not, why not? Reply Link to post Share on other sites More sharing options...
Eyas Posted May 3, 2009 Author Report Share Posted May 3, 2009 Depends which way you look at it.10P6 can both stand for:-the number of ways in which 6 people can occupy 10 different seats-the number of ways in which 6 seats can be assigned to 10 different people Reply Link to post Share on other sites More sharing options...
Forester Posted May 8, 2009 Report Share Posted May 8, 2009 (edited) If the order matters, use P. If order doesn't matter, use C. Edited May 8, 2009 by Forester Reply Link to post Share on other sites More sharing options...
Riptide Posted May 10, 2009 Report Share Posted May 10, 2009 (edited) Depends which way you look at it.10P6 can both stand for:-the number of ways in which 6 people can occupy 10 different seats-the number of ways in which 6 seats can be assigned to 10 different peopleOh, ok. Thank you for informing me of this. Edited May 10, 2009 by Riptide Reply Link to post Share on other sites More sharing options...
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