Bifalgorithm post · Brisk · Chapter 1

When are the numbers of combinations greatest and smallest?

When are the numbers of combinations greatest and smallest? (Brisk · Chapter 1) — "Also notice that the way to get the greatest number of combinations of n ite…

Ideas in this flowchart

Number of combinations of n items when choosing k
The greatest number of combinations occurs when k is half of n
Example: choosing books from a library
With 100 books, choosing 50 gives more combinations than choosing 5 or 95
Extreme endpoints always produce exactly one combination
Choosing no items: (n 0) = 1
There is only one way to choose nothing: come up empty
Choosing all items: (n n) = 1
There is only one way to choose everything: pick all the items

Bifalgorithm

Feed/

When are the numbers of combinations greatest and smallest?

Channel

Brisk

1 page

USR292600b83e2a

Ebook3w

"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."

Flowchart preview

👍

0 comments0 shares