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combinations and permutations pretty much covers it
If you wanted to check how many combinations there were when, say, 3 from 10 sent you a card
then from a 'n, choose r' type calc then n=10, r=3 and the number of combinations would be 120
https://www.calculatorsoup.com/calculators/discretemathematics/combinations.phpin your example, if you just have two choices then you'd probably most often find it illustrated as a binary tree 3 levels deep
3 people may or may not send me a Xmas card.
Sort of like:
Etc.