Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

distribution of balls

the number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty......give proper explaination plz

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: distribution of balls

Hi juan

Let us repesent the balls with zeros. Let us think of the bixes as they were glued together so that they look like compartments with 3 dividers between them. We can represent the balls and the dividers like this:

0000000000 | | |

Where the three lines are the dividers. Now we look at how many permutations we can make from the whole set of dividers and balls. Since there are 13 elements in total in that set we have 13! permutations,but since te balls are identical we must exclude their permutations by dividing by 10! and we do the same for the dividers because they are identical so the number of ways is:

13!/(10!*3!)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: distribution of balls

Hi juantheron;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathmatiKs

Member

Registered: 2012-04-14

Posts: 45

Re: distribution of balls

anonimnystefy
I think you miss something. Tell me if I'm wrong.

Says they have to be the 4 boxes full.

It means that the combination 000000|00|00| not allowed since the fourth box would be empty.
I would have to subtract these possible ways taking it to 000000|00|00 being "|" missing one of the stops.
And also when it is of the form 00000000|00||  and form 0000000000||| .
As would be empty boxes.

Last edited by mathmatiKs (2012-04-15 05:06:31)

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"... And as we let our own light shine, we unconsciously give other people permission to do the same. As we're liberated from our own fear, our presence automatically liberates others."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,167

Re: distribution of balls

And yet anonimnystefy has the same answer as bobbym.

Interesting.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: distribution of balls

Hi juantheron;

Forgot the constraint that there is no box empty. The formula is:

I believe the generating function is

Look at the coefficient of x^10, that is the answer.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: distribution of balls

If you wanted to do it the classic way you could just put one ball in each box and then work as though you had 6 balls left.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

YG

Guest

Re: distribution of balls

well u want no box to be empty put 1 ball in any of the box n freeze it n put remaining 9 balls in remaining boxes so the ans would be

r = no of balls
n = no of boxes

(r-1
    C
      n-1)