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Math Help - Permutation and Combination problem

  1. #1
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    Permutation and Combination problem

    The diagram shows a gird measuring 4 cm by 6 cm. The aim is to get from point A in the top left - hand corner to point B in the bottom right-hand corner by moving along the black lines either downwards or to the right. A single move is defined as shifting along one side of a single square, thus it takes you ten moves to get from A to B.

    sorry I haven't got the diagram here....

    a) How many different routes are possible?

    b) How many different routes are possible if you cannot move along the top line of the grid?

    c) How many different routes are possible if you cannot move along the second row from the top of the grid?


    2) a) the six faces of a number of identical cubes are painted in six distinct colours. How many different cubes can be formed?

    b) A die fits perfectly into a cubical box. How many ways are there of putting the die into the box?

    I can't solve these ARrrr, please help
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  2. #2
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    Quote Originally Posted by hkdrmark View Post
    The diagram shows a gird measuring 4 cm by 6 cm. The aim is to get from point A in the top left - hand corner to point B in the bottom right-hand corner by moving along the black lines either downwards or to the right. A single move is defined as shifting along one side of a single square, thus it takes you ten moves to get from A to B.

    sorry I haven't got the diagram here....

    a) How many different routes are possible?

    b) How many different routes are possible if you cannot move along the top line of the grid?

    c) How many different routes are possible if you cannot move along the second row from the top of the grid?
    Sorry i cant understand what you are saying


    Quote Originally Posted by hkdrmark View Post
    2) a) the six faces of a number of identical cubes are painted in six distinct colours. How many different cubes can be formed?
    6^6:Because each of the faces can be painted in 6 different ways and there are 6 faces


    Quote Originally Posted by hkdrmark View Post
    b) A die fits perfectly into a cubical box. How many ways are there of putting the die into the box?
    What has a die got to do with coloured cubes?
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  3. #3
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    Arrgghh can anyone help me ?

    These questions are from my text book, sorry I can't explain the question because I can't solve it!
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    Quote Originally Posted by Isomorphism View Post
    Sorry i cant understand what you are saying



    6^6:Because each of the faces can be painted in 6 different ways and there are 6 faces



    What has a die got to do with coloured cubes?
    and your answer for 2a is wrong... sorry
    it is 30
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  5. #5
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    Quote Originally Posted by hkdrmark View Post
    The diagram shows a gird measuring 4 cm by 6 cm. The aim is to get from point A in the top left - hand corner to point B in the bottom right-hand corner by moving along the black lines either downwards or to the right. A single move is defined as shifting along one side of a single square, thus it takes you ten moves to get from A to B.
    a) How many different routes are possible?
    b) How many different routes are possible if you cannot move along the top line of the grid?
    c) How many different routes are possible if you cannot move along the second row from the top of the grid?
    For part (a) you must count 4-Dís and 6-Rís. How can they be arranged?
    \frac {10!}{(4!)(6!)}?

    For part (b) you must count 3-Dís and 6-Rís. How can they be arranged?
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  6. #6
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    Quote Originally Posted by Plato View Post
    a) How many different routes are possible?
    b) How many different routes are possible if you cannot move along the top line of the grid?
    c) How many different routes are possible if you cannot move along the second row from the top of the grid?
    For part (a) you must count 4-Dís and 6-Rís. How can they be arranged?
    \frac {10!}{(4!)(6!)}?

    For part (b) you must count 3-Dís and 6-Rís. How can they be arranged?
    you are great! thanks!
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  7. #7
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    Quote Originally Posted by hkdrmark View Post
    and your answer for 2a is wrong... sorry
    it is 30
    Ya sorry...
    But I dont think it is 30 either...

    There are 6 faces. Each face can be colored in 6 different colors...
    I can either choose all colors same in 6 ways.
    I can either choose all colors except 1 same in 6 x 5C1 = 30 ways.
    It is already greater than 30
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  8. #8
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    Quote Originally Posted by Isomorphism View Post
    Ya sorry...
    But I dont think it is 30 either...

    There are 6 faces. Each face can be colored in 6 different colors...
    I can either choose all colors same in 6 ways.
    I can either choose all colors except 1 same in 6 x 5C1 = 30 ways.
    It is already greater than 30
    I got the answer already

    6! = amount of ways of change

    on a dice, let a face to be 1, then the opposite face must be another no., then the other 4 faces will change when we rotate the dice, which will result in 4 results ( 90--> 180--> 270 --> 360)
    and therefore the amount of repetitions is 6 * 4 = 24

    then therefore the answer is 6!/24 = 30
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