Subsets of A containing exactly 2 elements can be formed in the following ways.
A={1,2,3,4,5,6,7,8,9,10}S1=[{1,2},{1,3},{1,4},{1,5},{1,6},{1,7},{1,8},{1,9},{1,10}]→n1=9
S2=[{2,3},{2,4},{2,5},{2,6},{2,7},{2,8},{2,9},{2,10}]→n2=8
S3=[{3,4},{3,5},{3,6},{3,7},{3,8},{3,9},{3,10}]→n9=7
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S9={9,10}→n=1Therefore total number of subsets of A containing exactly two elements will be equal to
ntotal=ni=9+8+7+6+5+4+3+2+1
==45