Math CentralQuandaries & Queries


Question from vidya:

I am having a series of numbers eg.( 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
I can take any 5 digits eg(15,10,8,6,5) and it should not repeat and the summation should be any predefined static value . eg(44)
That is (15+10+8+6+5=44) . How many summation series will result 44 ?
My problem is how to find this using a formula or any other simpler automation method is there instead of checking one by one all the combinations.

Plz do help me... Thanks in advance


Your problem involves what is called a RESTRICTED PARTITION. I have not seen your particular problem, but it has probably been studied extensively. You might want to start with the Wikipedia page
(see especially restricted partitions) and follow the links to Young diagrams and anything else that seems helpful.


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