Some scientists claim that there are 7 colors in the rainbow: red, orange, yellow, green, blue, indigo, and violet.

7 families had a great idea to dress their children up in colored shirts to recreate a rainbow. Each family has exactly two children. Since this is such a monumental event, a family is very much hoping to have a child included in the rainbow recreation. Nevertheless, instead of carefully organizing the event, they believed in the power of randomness. So, they agreed to "Dress each child up in a random color from the rainbow" and hope everything would work out. Precisely, each of the fourteen children has probability 1/7 of getting any color from the rainbow, and each child's shirt color is chosen independently from the other thirteen.We will call a set of children happy if the set of children has exactly one child from each family is chosen, and each color of the rainbow is represented among these 7 children. Note that fora set to be happy, it must have exactly 7 children. Let H be a random variable denoting the number of happy sets of children.

What is the expected happiness, i.e. the expected value of H?