The objective is to determine whether there are two pairs of integers with the sum of 11, if seven integers are selected from the first 10 positive integers.

Partition the set A={1,2,3,4,5,6,7,8,9,10} into five disjoint subsets: {1,10},{2,9},{3,8},{4,7},{5,6}.

Observe that each of the integers in occurs in exactly one of the five subsets and that the sum of the integers in each subset add up to 11.
Thus, if 7 integers from are chosen, then by the pigeonhole principle, there exist two pairs that add up to 11.
Yes, there are two pairs of integers with the sum of 11, if seven integers are selected from the first 10 positive integers.The objective is to determine whether there are two pairs of integers with the sum of 11, if seven integers are selected from the first 10 positive integers.

Partition the set A={1,2,3,4,5,6,7,8,9,10} into five disjoint subsets: {1,10},{2,9},{3,8},{4,7},{5,6}.

Observe that each of the integers in occurs in exactly one of the five subsets and that the sum of the integers in each subset add up to 11.
Thus, if 7 integers from are chosen, then by the pigeonhole principle, there exist two pairs that add up to 11.
Yes, there are two pairs of integers with the sum of 11, if seven integers are selected from the first 10 positive integers.