My Math Forum Illustrating results of Binomial Coefficient calculation.

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August 6th, 2013, 12:13 AM   #1
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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!!!
Attached Images
 boxes2.jpg (30.8 KB, 191 views) boxes.jpg (37.3 KB, 191 views)

August 6th, 2013, 12:49 AM   #2
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From: Belgium

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Re: Illustrating results of Binomial Coefficient calculation

Quote:
 the 8 compartments
Your drawings have 64 compartiments so there is something wrong in your 'visualisation'

 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+"
") }
 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!

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