I need some help to create an R script that will solve the following problem:

• I have a list of products: A, B, C and D.
• I need to create baskets that contains several products.
• Each basket contains a total of 6 units of products and can contain between 2 & 4 unique products.
• Each basket must contains between 2 & 5 units of A, and between 0 & 1 unit of product B, C & D.
• The customer opens a basket. The probability to obtain a specific basket is determined by some weights.
• Therefore, baskets can be something like:
  enter image description here

What I need

• I need to determine the weights of each single basket…
  enter image description here
• …so the probabilities to obtain a specific product are the following:
  enter image description here

In other words: the customer always receives some units of product A; the probability to obtain a product B tends to 40%; the probability to obtain a product C tends to 5%…

I already have listed the possible combinations, but I am failing to:

• determine the minimum amount of baskets so the algorithm has enough degrees of freedom to calculate optimum weights for each basket.
• find a mathematical formula and R code (probably something related to matrix resolution, MASS package…) to calculate the weights (I need a mathematical approach since in real life I am working with more products, so an approach with a loop going through all the possibilities implies too many combinations).