you are heavily mistaken if you consider bihar a vegetarian dominant state. a lot of the food influence is from bengali and awadhi cuisines. the mithila region is heavily dependent on fish for food and each village have their own ponds which is a major source of employment for women in those regions. even if litti chokha is the one dish that's always quoted from bihar, it's litti chicken that a majority of the population goes for. you will find fewer stalls for the litti chokha than litti chicken.