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Line 57: − # 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
Permutations And Combinations (view source)
Revision as of 13:18, 10 July 2014
, 13:18, 10 July 2014→Hints for difficult problems
= Hints for difficult problems =
= Hints for difficult problems =
= Project Ideas =
= Project Ideas =