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Grade 12th passAlgebra

Let N be total nubers of subsets of A{ 1,2,3,4,5,6,7,8,9,10,11,12}have property that sum of any two elements of subset is not 9. Then value of N/144= ???

Profile image of Rakesh Kumar
8 Years agoGrade 12th pass
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1 Answer

Profile image of mycroft holmes
8 Years ago
The subset should not have as subsets {1,8}, {2,7}, {3,6}, {4,5} or unions of these sets.
 
Hence using the Principle of Inclusion-Exclusion the total number of such susbets 
 
=2^{12}-\binom{4}{1}2^{10}+\binom{4}{2}2^{8}-\binom{4}{3}2^{6}+\binom{4}{4}2^{4}
= 1296
 
The required answer is 1296/144 = 9
 
 

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