a) How many ways are there to pair up the elements of $\{1,2,\dots,14\}$ into seven pairs so that each pair has sum at least $15$? b) How many ways are there to pair up the elements of $\{1,2,\dots,14\}$ into seven pairs so that each pair has sum at least $13$? c) How many ways are there to pair up the elements of $\{1,2,\dots,2024\}$ into $1012$ pairs so that each pair has sum at least $2001$?