Let there be n balls and m urns.
1). If all balls are distinct and all urns are also distinct then number of ways in which the balls can be put in the urns is
2). If balls are all alike but urns are distinct then the number of ways are
3). If balls are distinct but urns are not then????
4) If both are alike then????
what is the solution to the last two?
For #3 you need to know about Stirling numbers of the second kind.
I am not sure exactly what #4 says.
If it means that both balls and urns are indistinguishable, the you need to partition n into m or fewer summons. EXAMPLE: If we have eight identical balls and five identical urns then P(8,5)=18.
well, i dont know what are stirling numbers of second kind.
can you suggest me some good text on combinatorics which treats the subject starting form level zero?
i am in college but am not a math major but i want to learn on my own so please help.