Permutation

[Saumyojit]

How many ways u can distribute 10 identical balls into 3 boxes ?
My apporach was :
B1 B2 B3
10 0 0 =3p1=out of 3 boxes placing 10 balls in 1 box
9 1 0 =3p2=out of 3 boxes placing 9 balls in box1 and 1 ball in box2
8 2 0 =3p2
8 1 1= 3p2 / 2!
7 3 0=3p2
6 1 3=3p3
7 2 1 =3p3
5 2 3=3p3
6 4 0=3p2
5 4 1 =3p3
4 4 2 =3p3/2!
3 3 4 =3p3/2!
2 2 6=3p3/2!

IS my approach wrong?

 

[Romsek]

This is a classic stars and bars problem.
[MATH]n=3,~k=10[/MATH]
[MATH]N=\dbinom{n+k-1}{n-1} = \dbinom{12}{2} = 66[/MATH]

 

[pka]

How many ways u can distribute 10 identical balls into 3 boxes ?
My apporach was :IS my approach wrong?

Once again this is a multi-set distribution., also known as a occupancy question.
The number of ways to place $\displaystyle N$ identical balls into $\displaystyle K$ distinct cells is $\displaystyle \dfrac{(N+K-1)!}{(N)!([K-1]!)}$.
You are making things very hard on yourself. That is such an easy formula to recall: stars&bars.
Just wait until you meet Stirling Numbers

 

[Dr.Peterson]

How many ways u can distribute 10 identical balls into 3 boxes ?
My apporach was :
B1 B2 B3
10 0 0 =3p1=out of 3 boxes placing 10 balls in 1 box
9 1 0 =3p2=out of 3 boxes placing 9 balls in box1 and 1 ball in box2
8 2 0 =3p2
8 1 1= 3p2 / 2!
7 3 0=3p2
6 1 3=3p3
7 2 1 =3p3
5 2 3=3p3
6 4 0=3p2
5 4 1 =3p3
4 4 2 =3p3/2!
3 3 4 =3p3/2!
2 2 6=3p3/2!

IS my approach wrong?

Not wrong, but far too much work.

The fact that you put 6 1 3 before 7 2 1 (and later didn't continue listing in decreasing order) suggests you aren't following an orderly way of listing possibilities, which increases the chance of a mistake.