In how many ways can two distinct subsets of the set A of k(k ≥ 2) elements be selected so that they have exactly two common elements.
Text Solution
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( k–2 –1)
Sol. Let the two subset be A & B
First select two element in k C 2 ways
Now remaining 'r' element for subset A are selected from (k – 2) elements and number of element for B from k – 2 – r elements
0 ≤ r ≤ k – 2
number of selection = k–2 C r .2 k–2–r
total number of selection
– 1,
Now every pair A, B is appearing twice
k C 2 
((2 + 1) k–2 –1)
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