
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 6th, 2013, 12:13 AM  #1 
Newbie Joined: Aug 2013 Posts: 7 Thanks: 0  Illustrating results of Binomial Coefficient calculation.
In regards to my previous post, I have calculated the result I need for my 'ball in a box' problem. Now, I'm trying to figure out a way I can see the results as an example. In my first example, I stated that there are 8 different ways you can place a single ball in an 8 compartment box. Now, if I were to visualise this, it might look like the example in the first attachment. Easy to see the results, right? Now, I'm trying to see the available results if I were to use 5 balls in the 8 compartments. Using the Binomial Coefficient formula, I know that there are 56 possible ways to display the results. So, does anyone have any tips as to how I can visualise these results? To start, I put 5 balls in a row, then moved the last one over to the next compartment. This yielded 4 results (see the 2nd attachment) I am now trying to decide the best way to progress, or even if I should  is this method ideal? Is there an easier way to do it? If anyone has any ideas on how I can do this without giving me a headache, I'd love to hear it! Thankyou!!! 
August 6th, 2013, 12:49 AM  #2  
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Illustrating results of Binomial Coefficient calculation Quote:
 
August 6th, 2013, 01:00 AM  #3 
Newbie Joined: Aug 2013 Posts: 7 Thanks: 0  Re: Illustrating results of Binomial Coefficient calculation
Sorry, I should have specified  each numbered row represents a different box of compartments, so in the first example there are 8 boxes on top of each other. In the second example, there are 4.

August 6th, 2013, 01:26 AM  #4 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Illustrating results of Binomial Coefficient calculation Code:  •  •  •  •  •  _  _  _   •  •  •  •  _  •  _  _   •  •  •  •  _  _  •  _   •  •  •  •  _  _  _  •   •  •  •  _  •  •  _  _   •  •  •  _  •  _  •  _   •  •  •  _  •  _  _  •   •  •  •  _  _  •  •  _   •  •  •  _  _  •  _  •   •  •  •  _  _  _  •  •   •  •  _  •  •  •  _  _   •  •  _  •  •  _  •  _   •  •  _  •  •  _  _  •   •  •  _  •  _  •  •  _   •  •  _  •  _  •  _  •   •  •  _  •  _  _  •  •   •  •  _  _  •  •  •  _   •  •  _  _  •  •  _  •   •  •  _  _  •  _  •  •   •  •  _  _  _  •  •  •   •  _  •  •  •  •  _  _   •  _  •  •  •  _  •  _   •  _  •  •  •  _  _  •   •  _  •  •  _  •  •  _   •  _  •  •  _  •  _  •   •  _  •  •  _  _  •  •   •  _  •  _  •  •  •  _   •  _  •  _  •  •  _  •   •  _  •  _  •  _  •  •   •  _  •  _  _  •  •  •   •  _  _  •  •  •  •  _   •  _  _  •  •  •  _  •   •  _  _  •  •  _  •  •   •  _  _  •  _  •  •  •   •  _  _  _  •  •  •  •   _  •  •  •  •  •  _  _   _  •  •  •  •  _  •  _   _  •  •  •  •  _  _  •   _  •  •  •  _  •  •  _   _  •  •  •  _  •  _  •   _  •  •  •  _  _  •  •   _  •  •  _  •  •  •  _   _  •  •  _  •  •  _  •   _  •  •  _  •  _  •  •   _  •  •  _  _  •  •  •   _  •  _  •  •  •  •  _   _  •  _  •  •  •  _  •   _  •  _  •  •  _  •  •   _  •  _  •  _  •  •  •   _  •  _  _  •  •  •  •   _  _  •  •  •  •  •  _   _  _  •  •  •  •  _  •   _  _  •  •  •  _  •  •   _  _  •  •  _  •  •  •   _  _  •  _  •  •  •  •   _  _  _  •  •  •  •  •  
August 6th, 2013, 01:42 AM  #5 
Newbie Joined: Aug 2013 Posts: 7 Thanks: 0  Re: Illustrating results of Binomial Coefficient calculation
Wow, thanks! How did you do that?

August 6th, 2013, 01:53 AM  #6 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Illustrating results of Binomial Coefficient calculation
I wrote a quick javascript code for it. here is the code: Code: function a() { //document.write (" •  _  _  _  _  _  _  _ "); for (i1=0;i1<4;i1++) { for (i2=i1+1;i2<5;i2++) { for (i3=i2+1;i3<6;i3++) { for (i4=i3+1;i4<7;i4++) { for (i5=i4+1;i5<8;i5++) { disp(i1,i2,i3,i4,i5); } } } } } } function disp(i1,i2,i3,i4,i5) { var out=new Array(); for (i=0;i<8;i++) { out[i]="_"; } out[i1]="•"; out[i2]="•"; out[i3]="•"; out[i4]="•"; out[i5]="•"; var text=""; for (i=0;i<8;i++) { text+=" "+out[i]+" "; } document.write(""+text+"</br>") } 
August 6th, 2013, 02:04 AM  #7 
Newbie Joined: Aug 2013 Posts: 7 Thanks: 0  Re: Illustrating results of Binomial Coefficient calculation
Amazing! Thank you so much for your help! 

Tags 
binomial, calculation, coefficient, illustrating, results 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Binomial theorem (Finding coefficient of X^{3n}  Punch  Probability and Statistics  3  June 5th, 2012 06:21 PM 
Binomial distribution calculation, need help  twobeatsoff  Advanced Statistics  2  February 13th, 2012 10:26 AM 
Binomial Coefficient problem  pikachu26134  Number Theory  3  July 26th, 2011 07:03 PM 
Binomial coefficient (padic)  sunflower  Number Theory  0  April 2nd, 2011 07:15 AM 
Binomial Coefficient Proof  coolhandluke  Applied Math  1  March 26th, 2010 04:55 PM 