Here's a cute idea combining modelling and combinatorics - what if, calculating lottery probabilities, you model the lottery leaving out some possible tickets? Does it change your conclusions? I run through the calculations for ignoring tickets that are all squares, tickets that are all odds, and tickets with a 7.

An incorrect model of the lottery, and when it doesn’t matter https://aperiodical.com/2022/04/an-incorrect-model-of-the-lottery-and-when-it-doesnt-matter/

The idea is from Matt Parker on A Problem Squared 032.