Difference between revisions of "Permutations And Combinations"

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= Hints for difficult problems =
 
= Hints for difficult problems =
#  How many 1) lines`
 
2) Triangles can be drawn through 8 points on a circle
 
 
Interpetation:
 
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.
 
 
Methods:
 
1) visual method
 
2) arithmetic way
 
 
Concepts:
 
1. circle
 
2. co-linear and non co-linear points
 
3.  difference bet'n line, ray and segment
 
4.  points require to draw a triangle
 
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.
 
6. Expantion of Factorial
 
 
Solution:
 
 
1. for drawing lines we need atleast two points then selecting 2 points out of 8 given we have
 
 
                                <br> = arrangements
 
 
 
      <br>n!
 
          <br> =----------- ( students should know the formula)
 
    <br>(n-r)! r!
 
 
                        <br>    8!
 
        <br>  = ----------- (substituting the values into the formula)
 
            <br>  (8-2)! 2!
 
 
      <br>8!
 
          <br>= ----------- (simplification)
 
              <br>6! 2!
 
 
<br>
 
    <br>                          8*7*6*5*4*3*2*1
 
<br>           =--------------------------
 
<br>       6*5*4*3*2*1*2*1
 
 
<br>           =4*7
 
<br>
 
<br> = 28
 
 
<br> 2. for drawing a triangle we need 3 non co-linear points then selecting 3 points out of 8 given we have
 
    <br>                            = arrengements
 
 
 
 
 
<br>       n!
 
<br>           =----------- ( students should know the formula)
 
<br>     (n-r)! r!
 
 
            <br>                  8!
 
        <br>          = ----------- (substituting the values into the formula)
 
    <br>        (8-3)! 3!
 
 
<br>        8!
 
          <br>= ----------- (simplification)
 
              <br>5! 3!
 
 
<br>
 
    <br>                          8*7*6*5*4*3*2*1
 
<br>           =--------------------------
 
<br>       5*4*3*2*1*3*2*1
 
 
<br>           =8*7
 
 
<br>           = 56
 
  
 
= Project Ideas =
 
= Project Ideas =

Revision as of 07:48, 10 July 2014

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