Let S be the set of all symmetric matrices of order 
, all of whose elements are either 0 or 1. If five of these elements are 1 and four of them are 0 , then the number of matrices in S is 
.
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Let 
. In a symmetric matrix the 
th element is same as 
th element for 
. That is, upper and lower parts of the principal diagonal are reflections of each other through the principal diagonal. Hence the principal diagonal of A must have three l's or two 0 's and a single because A has five Ts and four 0 's. If all the three diagonal elements are 1, the number of such matrices is 
. If two diagonal elements are zeros and one is 1, then the number of such matrices is 
. Therefore, total number of matrices in
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