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by shashank.ism » Mon Feb 15, 2010 10:38 pm
The set S has 5 elements. In how many ways can one select two (possibly identical) subsets of S whose union is S?
A) 32
B) 63
C) 64
D) 93
E) 122
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by harsh.champ » Thu Feb 18, 2010 5:00 am
shashank.ism wrote:The set S has 5 elements. In how many ways can one select two (possibly identical) subsets of S whose union is S?
A) 32
B) 63
C) 64
D) 93
E) 122
Let the elements be [a,b,c,d,e]
Now, we have to select (3,3);(4,4);(5,5) elements.
For (3,3) :-The common element in both can be selected in 4C2 x 5 ways.
For (4,4) :-1 element differing can be selected in 5C3 ways.[(1,2,3,4) and (1,2,3,5)]
For (5,5) :- We have only 1 way.

But,I am not getting the answer.Can you post the soln.?
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