Number of Non-Negative Integer solutions of the equation x + y + z = 10 | General Case Explained

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In this video, we count how many non-negative integer solutions are there for the equation x+y+z=10. In general, if x+y+z=n, how many such solutions will be there? That also explained. Also explained in general, the number of non negative integer solutions of the equation x_1 + x_2 +... + x_r = n.
A generalized idea of how to attack this problem is mentioned.

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  2. number of non negative integer solutions for the equation
  3. number of non negative integer solutions of the equation x y z=10
  4. counting the number of non negative integer solutions for equation
  5. distributing identical objects
  6. combinatorics
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Комментарии
Автор

Please, solve this example.
*How many positive integer solutions of the equation 2x + 3y + 4z = 24.

Thank you.

Shahadat_Ome
Автор

1. Three variables x, y, z have sum of 30.
All three of them are non- negative
integers. If any two variables don't have
same value and exactly one variable has
a value less than or equal to three, then
find the number of possible solution for
variables.

peramvenkatasivapavani
Автор

The marker sound making uncomfortable, I hope some might have the same problem. May be Change marker or board would be nicer.

pavanfernandes