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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:Pepperoni (a) Sausage (b) Pepperoni and Sausage (ab) If there are three toppings, I get seven options (I think)Pepperoni (a) Sausage (b) Mushrooms (c) Pep and Sausage (ab) Pep and Shrooms (ac) Sausage and Shrooms (bc) The Works (abc) Four toppings = 15 options (I think)a, b, c, d ab, ac, ad, bc, bd, cd abc, abd, acd, bcd abcd Five toppings = 30 options (I think...)a, b, c, d, e ab, ac, ad, ae, bc, bd, be, cd, ce, de abc, abd, abe, acd, ace, ade, bcd, bce, bde, cde abcd, abce, abde, bcde abcde I can't find a pattern! 15 = 4!-(3^2) (i.e., n!-((n-1)^2))) 30 = 5!/(n-1) Ugh! How am I not looking at this right?
 July 24th, 2017, 09:10 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 You missed acde. If you include "no toppings", the results become 4, 8, 16, 32, etc. Thanks from Alonzo Mosley
 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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