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= Hints for difficult problems =
 
= Hints for difficult problems =
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#  How many 1) lines`
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2) Triangles can be drawn through 8 points on a circle
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Interpetation:
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drawing lines and triangle using the 8 points which are  on a circumference of a  circle (irrespective of the position on circumference , may be equally spaced or not) . And students should identify whether the problem is of arrengement  or selection of objects.
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Methods:
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1) visual method
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2) arithmetic way
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Concepts:
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1. circle
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2. co-linear and non co-linear points
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3.  difference bet'n line, ray and segment
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4.  points require to draw a triangle
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5.  difference bet'n arrengements and selection for eg. If A and B are two objects then AB and BA are different arregements where as AB          and BA are both same when it comes to selection.
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6. Expantion of Factorial
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Solution:
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1. for drawing lines we need atleast two points then selecting 2 points out of 8 given we have
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                                <br> = arrangements
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      <br>n!
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          <br> =----------- ( students should know the formula)
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    <br>(n-r)! r!
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                        <br>    8!
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        <br>  = ----------- (substituting the values into the formula)
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            <br>  (8-2)! 2!
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      <br>8!
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          <br>= ----------- (simplification)
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              <br>6! 2!
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<br>
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    <br>                          8*7*6*5*4*3*2*1
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<br>           =--------------------------
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<br>       6*5*4*3*2*1*2*1
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<br>           =4*7
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<br>
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<br> = 28
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<br> 2. for drawing a triangle we need 3 non co-linear points then selecting 3 points out of 8 given we have
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    <br>                            = arrengements
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<br>       n!
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<br>           =----------- ( students should know the formula)
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<br>     (n-r)! r!
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            <br>                  8!
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        <br>          = ----------- (substituting the values into the formula)
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    <br>        (8-3)! 3!
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<br>        8!
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          <br>= ----------- (simplification)
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              <br>5! 3!
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<br>
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    <br>                          8*7*6*5*4*3*2*1
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<br>           =--------------------------
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<br>       5*4*3*2*1*3*2*1
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<br>           =8*7
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<br>           = 56
    
= Project Ideas =
 
= Project Ideas =
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