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Sets-good question

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by rishab1988 » Mon Nov 29, 2010 1:53 am
The total number of 2 element intersections possible in 2 element a set is 1..Let a denote the total number regions that consist of intersection of 2 elements in a 4 element set and b denote the total number of regions that consist of intersections of two elements in a 11 element set,and c denote the sum of a and b,then c is equal to:

A) 25
B) 36
C) 61
D) 74
E) 3^12
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by kvcpk » Mon Nov 29, 2010 2:42 am
The total number of 2 element intersections in an n-element set = nc2
Hence for a 4 element set, The total number of 2 element intersections = 4c2 = 6
For a 11 element set, The total number of 2 element intersections = 11c2 = 55

Hence total = 55+6 =61
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by rishab1988 » Mon Nov 29, 2010 2:52 am
You have solved it correctly.

I wanted to design a question that involved testing combinatorics in sets,as I haven't seen,till now,any of these questions.Sometimes people get put off by sets and combinations in the same question..
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