Please provide an in depth, detailed response to the image below. This is applied maths

A bag contains marbles of n different colors in equal number. Two marbles are considered indistinguishable if and only if they have the same color. Knowing that there are more than three marbles of each color in the bag, and that there are at least 20 different ways to pick 3 marbles from the bag, what is the least possible value of n