Problem Analysis #15

[THOUGHT] We need to compute the number of ways to choose 2 unordered pairs from 15 unordered pairs (since the set has 6 elements, the number of unordered pairs is C(6,2)=15). The relation must be reflexive (so the diagonal is fixed, 6 elements) and symmetric (so we must add entire unordered pairs, each contributing 2 elements). We need exactly 10 elements, so 10-6=4 off-diagonal elements, which requires 2 unordered pairs. The number of ways is C(15,2)=105. [/THOUGHT] [PYTHON] print(15 * 14 // 2) [/PYTHON]

[THOUGHT] The result is 105. [/THOUGHT] \boxed{105}

[THOUGHT] The Python code computed the combination of 15 items taken 2 at a time as 105. This matches the required calculation for the number of ways to choose 2 unordered pairs from the 15 possible pairs in a 6-element set. The result is 105. [/THOUGHT] \boxed{105}