The parents were asked on "Today" why, given all the trouble families like the Gosselins ("Jon and Kate Plus Eight") have seen, they were doing the show. Betty Hayes gave what I thought was a credible and realistic answer.
One of their children has cerebral palsy, and her mom said she thought the show would provide them with the means to give that child possibilities she might not otherwise have. I took that to mean that she thought the money TLC paid them would allow the parents to provide their daughter with such resources and opportunities. The father is a police officer.
Here's the TLC Web site for the show about the Hayes family of two parents and 10 kids - Betty and Eric, the twins, the twins, and the sextuplets.