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July 24th, 2017, 08:42 AM  #1 
Newbie Joined: Jul 2017 From: Seattle Posts: 2 Thanks: 0  Combinations with Variable r
Boy there are lots of different questions about combinations on this site, but none seem to match mine. How do I figure number of combinations of n items  no repeats  but there is no limit on r, and order doesn't matter? In other words, think of a pizza menu. If there are two potential toppings, there are three options:
If there are three toppings, I get seven options (I think)
Four toppings = 15 options (I think)
Five toppings = 30 options (I think...)
I can't find a pattern! 15 = 4!(3^2) (i.e., n!((n1)^2))) 30 = 5!/(n1) Ugh! How am I not looking at this right? 
July 24th, 2017, 09:10 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,542 Thanks: 1751 
You missed acde. If you include "no toppings", the results become 4, 8, 16, 32, etc.

July 24th, 2017, 09:19 AM  #3 
Newbie Joined: Jul 2017 From: Seattle Posts: 2 Thanks: 0 
Arghhh!!! I DID!!! ARGGGHH!!.. So, (2^n)1 Argh. Yes. Thanks. Wow, that hurt. 

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combinations, variable 
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