Answer to Question #28388 in Statistics and Probability for matt

Question

Suppose there are 3 sets (A,B,C) of 13 unique integers ranging from 1 - 39. Within these 3 sets every number between 1 and 39 is represented and not repeated. The 39 numbers are randomly distributed among the 3 sets. If I were to randomly select 5 non-repeating numbers between 1 - 39, how would I find the probability that all 5 would fall within one of the sets? Or that 4 numbers would fall within one set, or 3 numbers, etc? How would I find the total possible outcomes/distribution of how 5 randomly picked numbers would fall within these 3 sets?