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June 13th, 2011, 03:02 AM  #11 
Senior Member Joined: Feb 2010 Posts: 711 Thanks: 147  Re: Probability
The original poster's question was "three letters are selected at random from the word BIOLOGY. Find the number of ways in doing this". If the original poster's intent is that BOO is the same as BOO and that BLY is the same as LYB, then the answer is 25. If the original poster's intent is that BOO is the same as BOO but that BLY is different from LYB, then the answer is 135. If the original poster's intent is that BOO is different from BOO and BLY is different from LYB and the answer is then 210. 
June 13th, 2011, 05:07 AM  #12  
Senior Member Joined: Feb 2010 Posts: 711 Thanks: 147  Re: Probability Quote:
but there are two ways to choose OO.  
June 14th, 2011, 02:57 AM  #13  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Probability Quote:
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June 14th, 2011, 03:16 AM  #14  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Probability Quote:
It's 4! = 24, and I don't feel like writing all those out, but you get the point that I'm saying the two's O's there aren't the same ones. And neither are the two N's. Granted it will look alike if you flip those O's around. But I may not be looking at the same tile you are. Let's say instead we each have an N. If we traded, they'd look the same, but they wouldn't be the same tiles, so that's a different way of placing them. They may look alike, and from that standpoint neither of us cares which tile it happens to be. If I desparately need an N to make a cool word, I really don't care which one I get. But if I want to know the probability of getting one, then they have to become distinctive  if there's say 4 of them total, then I could pick any of the 4 and there would be 4 different ways to pick one.  
June 14th, 2011, 04:43 AM  #15  
Senior Member Joined: Feb 2010 Posts: 711 Thanks: 147  Re: Probability Quote:
I just reached in and pulled out B,O,L. Which one was it? The first O or the second O? If you are calculating probability, then BOL has frequency 2 since there are two O's. However if you are just counting the ways that you can pull three tiles out of the hat then there is only the one outcome.  
June 14th, 2011, 06:09 AM  #16  
Senior Member Joined: Feb 2010 Posts: 711 Thanks: 147  Re: Probability
I think I see where the area of disagreement is arising. The original poster's question was Quote:
As far as NOON goes, the answer is . This is a standard high school problem. For the technique, I refer you to Applied Combinatorics by Fred Roberts, Applied Combinatorics by Alan Tucker, or Enumerative Combinatorics by Richard Stanley.  
June 14th, 2011, 06:16 PM  #17  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Probability Quote:
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Let me ask you one more question: If there were 3 white marbles in a bag, how many ways are there for you to pick one white marble?  
June 14th, 2011, 06:41 PM  #18  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Probability Quote:
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Why does "number of ways" suddenly mean something completely different if we aren't doing a probability? In this problem, when you go to figure the probabilities presented, that 35 has to go in the denominator. In most problems I've seen, if they ask the "number of ways" something can be done prior to asking for a probability, they're kind of taking it one step at a time and "setting you up" for getting the probability. The "number of ways" to pick 3 letters has to go into the denominator. Why should it mean something different when they first asked the "number of ways" to do this? Where and how did that meaning change? (Which is a good thing to ask whoever put that question/solution together.)  
June 14th, 2011, 07:05 PM  #19 
Senior Member Joined: Feb 2010 Posts: 711 Thanks: 147  Re: Probability
Applied Combinatorics by Fred Roberts, PrenticeHall (ISBN:0130393134) P. 50 #8 How many different "words" can be formed using all the letters of the word renegotiate? Answer: 
June 14th, 2011, 08:36 PM  #20 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Probability
That's an entirely different thing. Age using one of the e's is the same word as age using the 2nd e or the 3rd e. That isn't the same question at all. Being the "same word" is in a sense the same as what I mean by the "way it looks." But even though "age" would be the same word regardless of which e you used, aren't there THREE WAYS to form it? "How many ways" and "how many words can you make" are not the same question! Not to mention that if you're making words, then AGE isn't the same as GEA. The problem didn't ask how many words you could make out of biology. Nor would BIG and GIB be two different things in the problem. So your example is an entirely different situation. You haven't answered any of the questions I've asked you. I asked them so that you would stop and think about it. You're too busy using examples that are entirely different things just to prove your answer. I have no issue continuing this discussion. But if you aren't addressing anything I'm saying or answering the questions I'm asking you to think about, you're just being an annoyance. Try addressing the questions I have posed. Is that blood I see dripping off the back of my head.... 

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