Concept
When are the numbers of combinations greatest and smallest?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Also notice that the way to get the greatest number of combinations of n items is for k to be half of n . If we have 100 books in our library, there are a lot more ways to check out 50 of them then there are to check out only 5, or to check out 95. Strange but true. Lastly, make sure you understand the extreme endpoints of this phenomenon. ( n 0 ) and ( n n ) are both always 1, no matter what n is. That’s because if you’re picking no items, you have no choices at all: there’s only one way to come up empty. And if you’re picking all the items, you also have no choices: you’re forced to pick everything."
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