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Math Help - Arrangements

  1. #1
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    Arrangements

    Dear All,

    I have few questions on probability, that's

    1) sunitha wants to make a necklace. she has 8 beads how many different choices does she have?
    2)from city A to B there are 3 different roads, from B to C there are 5, from C to D there are 2.Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order.In how many ways can he complete his journey if he has to take a different while coming back than he did while going?
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  2. #2
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    Quote Originally Posted by vijayayarra View Post
    1) sunitha wants to make a necklace. she has 8 beads how many different choices does she have?
    Only one if all the beads are alike.
    Last edited by mr fantastic; September 21st 2009 at 08:12 PM. Reason: Fixed quote
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  3. #3
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    Hello, vijayayarra!

    Both problems are poorly worded.
    I must make some guesses . . .


    1) Sunitha wants to make a necklace. She has 8 beads.
    How any different choices does she have?

    I will assume that there are 8 distinguishable beads,
    . . perhaps of 8 different colors.
    I will also assume that her necklace will have all 8 beads,
    . . and that the question is: "How many different necklaces can be made?"

    Placing 8 items in a circle, there are: . 7! ways.

    But half of them are mirror-images of the other half.

    Therefore, there are: . \frac{7!}{2} \:=\:2520 possible necklaces.




    2) From city A to B there are 3 different roads,
    from B to C there are 5, and from C to D there are 2.
    Laxman has to go from city A to D attending some work
    in cities B and C on the way and has to come back in the reverse order.

    In how many ways can he complete his journey if he has to
    take a different route while coming back than he did while going?

    Going from A to D, there are: . 3 \times 5 \times 2 \:=\:30 choices.


    Now what is meant by "a different route"?


    If it means that no road can be used more than once,
    then on the return trip, there are:
    . . 1 choice for D-to-C,
    . . 4 choices for C-to-B,
    . . 2 choices for B-to-A.

    Hence, there are: . 1 \times 4 \times 2 \:=\:8 choices for the return trip.


    If "a different route" means even slightly different, then the trip from D to A
    . . must not be exactly the same as the route from A to D.
    Then there are: . 30 - 1 \:=\:29 choices for the return trip.

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  4. #4
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    circular probability

    Hello,

    1) sunitha wants to make a necklace. she has 8 beads how many different choices does she have?
    Ans. 1200
    2)from city A to B there are 3 different roads, from B to C there are 5, from C to D there are 2.Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order.In how many ways can he complete his journey if he has to take a different while coming back than he did while going?
    Ans.870

    Sorry above ones are the correct answers but I don't understand the logic behind that.
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