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Grade: 12th pass

                        

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= ???

2 years ago

Answers : (1)

mycroft holmes
272 Points
							
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
 
 
2 years ago
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