AravindG
  • AravindG
find the no: of integral solutions of inequation x+y+z+u<=65
Mathematics
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
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anonymous
  • anonymous
0 is included?
anonymous
  • anonymous
I can do this using binomial coefficients.
AravindG
  • AravindG
i dont know tht fool

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anonymous
  • anonymous
Using stars and bars, the answer is given by \[ \huge \sum \limits_{n=0}^{65} \binom{n+3}{3} \]
anonymous
  • anonymous
can't wait to see this
anonymous
  • anonymous
stars and bars??
AravindG
  • AravindG
hw?
anonymous
  • anonymous
http://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)
anonymous
  • anonymous
this question is like putting three bookmarks in a book
anonymous
  • anonymous
how cool is that? stars and bars, nice visual!
anonymous
  • anonymous
Yeah it's coool :D
AravindG
  • AravindG
coool
anonymous
  • anonymous
One can also think logically and get the solution .. say you have x+y+z+u <= k (some integer) and you have to find the number of solutions then it is like finding the number of ways where k sweets can be distributed to 4 kids and total sweets distributed may not be equal to k. Now lets imagine a situation where we have 4 women and k men. How many ways of arranging them? (4+k)!/(4!*k!) Now say I say that all men who come to the left of any woman are given to that woman (not literally) .. then we have solved our distribution problem and hence our equation.. so I believe the answer should be 69!/(4!*65!)
anonymous
  • anonymous
@shaan_iitk How do you think stars and bars work? That is exactly the same thing you elaborated.
anonymous
  • anonymous
means?
anonymous
  • anonymous
Sorry but I am not aware of stars and bars ..
anonymous
  • anonymous
I have posted the url before.
anonymous
  • anonymous
okk .. I didn't look at that.. I only looked at your expression which was in summation form.. I thought logically we don't need that summation..

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