This is a variation of the coin change problem. Where,
Given N coins with values : (5,10,20,50)
And weight having weights/probabilities W: (0.1, 0.5, 0.3, 0.1)
What are the number of possible combinations, to make a sum : S = 100
whilst preserving the overall probability of each coin type. The same coin can be used multiple times. However, for example if 5 is used 10 times out of 100 coins to create the total S=100, then the probability is still 0.1. But if 5 is used 20 times in a solution to create S=100, then the prob(5) = 0.2, which is wrong.
Is there a similar variation to the coin-change problem ?
Is there a solution to this ? is it NP-hard ?
thanks