What I think we need to use $n+r-1\choose{r-1}$ for the pair $x+y=100$ I tried something like this there are total 24 pairs whose sum is 100 and 49 total odd so first selection will be $49\choose24$
After that i am stumped what to do ?
Please help
2026-04-03 14:22:26.1775226146
double selection probability
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Hint:
Can you construct an example in which no two element sum is equal to $100$?
Can you construct a set with less than 26 elements with no two elements sum is equal to $100$?
Feel free to ask for more clarification :)