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January 5th, 2013, 04:17 AM  #1 
Newbie Joined: Jan 2013 Posts: 12 Thanks: 0  A fairly basic counting problem that I'm drawing a blank on.
Hi all, I hope I'm posting this in the correct forum: The question is this: An ice cream store has 20 different flavours. In how many ways can we order a dozen different ice cream cones, if each cone has 2 different flavours ? If it was just 12 different cones from 20 different flavours, I would go C(20,12) = 125,970 but it's the "if each cone has 2 different flavours that I'm drawing a blank on. I imagine I'll feel like an idiot when it's pointed out, but any help would be much appreciated. Thank you. 
January 5th, 2013, 08:56 AM  #2 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: A fairly basic counting problem that I'm drawing a blank
i believe you just have to multiply that number with 20*19 because that's the amount of ways you can get 2 different flavours and divide by 2 since all combinations have been taken twice (such as {lemon,vanilla} is the same as {vanilla, lemon} ) so 125,970*190= 23,934,300 
January 5th, 2013, 09:00 AM  #3 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: A fairly basic counting problem that I'm drawing a blank 
January 5th, 2013, 10:19 AM  #4 
Senior Member Joined: Dec 2012 Posts: 372 Thanks: 2  Re: A fairly basic counting problem that I'm drawing a blank
This is what I think. First choose 12 from 20, which is 20_C_12. Next, for each cone you have 19 degrees of freedom left so multiply by 19^12. Answer should be (20_C_12) x (19^12).

January 5th, 2013, 10:55 AM  #5 
Senior Member Joined: Dec 2012 Posts: 372 Thanks: 2  Re: A fairly basic counting problem that I'm drawing a blank
Sorry, I was in error. Mr Zardoz has it correct

January 5th, 2013, 02:19 PM  #6  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: A fairly basic counting problem that I'm drawing a blank summsies! The word "different" makes the problem trickier. Quote:
 
January 5th, 2013, 09:23 PM  #7  
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: A fairly basic counting problem that I'm drawing a blank Quote:
it should be 3345763705175979360  
January 6th, 2013, 01:12 AM  #8 
Newbie Joined: Jan 2013 Posts: 12 Thanks: 0  Re: A fairly basic counting problem that I'm drawing a blank
Thanks to all who replied: Soroban, yes it was definitely the wording of different cones each with different flavours that tripped me up. These sneaky Math profs, hey So just to recap so I understand: From 20 different flavours, we're choosing 2 flavous per cone, giving us 190 possible combo's there, and then from that 190 possible combinations, we're making 12 different cones. I think that makes sense. Thanks again to all for your input !

January 6th, 2013, 01:21 AM  #9  
Newbie Joined: Jan 2013 Posts: 12 Thanks: 0  Re: A fairly basic counting problem that I'm drawing a blank Quote:
 
January 6th, 2013, 02:11 AM  #10 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: A fairly basic counting problem that I'm drawing a blank [color=#000000]Soroban's solution is correct![/color] 

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