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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
File Type: jpg boxes2.jpg (30.8 KB, 191 views)
File Type: jpg boxes.jpg (37.3 KB, 191 views)
rdam81 is offline  
 
August 6th, 2013, 12:49 AM   #2
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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'
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August 6th, 2013, 01:00 AM   #3
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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.
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August 6th, 2013, 01:26 AM   #4
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Re: Illustrating results of Binomial Coefficient calculation

Code:
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gelatine1 is offline  
August 6th, 2013, 01:42 AM   #5
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Re: Illustrating results of Binomial Coefficient calculation

Wow, thanks! How did you do that?
rdam81 is offline  
August 6th, 2013, 01:53 AM   #6
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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>")
}
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August 6th, 2013, 02:04 AM   #7
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Re: Illustrating results of Binomial Coefficient calculation

Amazing! Thank you so much for your help!
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