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Number of ways to distribute N balls into K boxes with a special condition

Revision en1, by van_persie9, 2019-08-25 00:14:57

Recently I came across a question in which we had to find the no. of ways to distribute N balls into 3 boxes such that the number of box getting maximum no. of balls is exactly 1.

For example

  • if N=2, ans is 2 : {2,0,0},{0,2,0},{0,0,2}

  • if N=3, ans is 9 : {3,0,0},{0,3,0},{0,0,3},{3,2,1},{3,1,2},{1,3,2},{2,3,1},{1,2,3},{2,1,3}

Now, since the number of boxes here is only 3, I was able to solve the question by observation and basic maths(Arith. Prog.) My query is how to solve the above question if the number of boxes is K?

Tags #math, #combinatorics

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en1 English van_persie9 2019-08-25 00:14:57 620 Initial revision (published)