MathDB

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

C2