Let the set of all relations R on the set \ a, b, c, d, e, f\ ,...

Let the set of all relations

R

on the set

\{a, b, c, d, e, f\}

, such that

R

is reflexive and symmetric, and

R

contains exactly 10 elements, be denoted by

S

. Then the number of elements in

S

is ______ $Let the set of all relations R on the set \ a, b, c, d, e, f\ , such that R is reflexive and symmetric, and R contains$

Correct answer

Step-by-step solution

$Let the set of all relations R on the set \ a, b, c, d, e, f\ , such that R is reflexive and symmetric, and R contains$
For relation to be reflexive all the diagonal elements must be taken and out of remaining 30 elements there are 15 pairs and we need 2 pairs such that R contains exactly 10 elements and is both reflexive and symmetric.

\therefore

number of ways

={ }^{15} \mathrm{C}_2=105

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