[INST] Two different numbers are randomly selected from the set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. The probability that their sum is 12 would be greater if the number n had first been removed from set S. What is the value of n?/n [/INST]  ###Response: All of the integers in the set S have exactly one complementary number, 12-x, such that their sum is 12, except for the number 6. Because 6+6= 12, and the two numbers chosen are distinct, removing 6 will not eliminate any of the pairs that sum to 12, and it will reduce the total number of pairs possible. So n=6.