Regardless of which of these shows you watch, if any, you'll easily understand how these connect.
1. The Big Bang Theory
Ecology. Bazinga. It's Physics.
The main character is Sheldon Cooper who is a physicist who has a Doctorate degree in Physics and does a variety of research as well. He tries to teach Penny and Leonard about why certain theories exist, such as Newton's Laws of motion, or other theories by Galileo or Nicolas Copernicus.
2. Two Broke Girls
Business.
The lead characters in this show are Caroline Channing and Max Black, two women who are trying to start a cupcake business but have to work multiple jobs for many hours each day to make enough money to start the business.
3. Are You Smarter Than A Fifth Grader?
Inclusive Early Childhood Education.
This game show has adult contestants competing for monetary winnings and they have to show that they have just as much knowledge, but more knowledge, than a fifth grader, and they have to answer questions that range from 1st-grade level material to 5th-grade level material. The competitors are portrayed to be students who haven't learned the importance of being prepared since they're allowed to cheat a couple of times, a big no-no in school.
4 (and 5). The Bachelor (and The Bachelorette)
Psychology.
On the show, there's either one girl ("Bachelorette") or one guy ("Bachelor") who is serially dating 25 beautiful women or 25 handsome men and has ultimate power in this dating game. The women/men get eliminated as the season continues, and there's a lot to process and understand about the thoughts that the Bachelorette or Bachelor experiences. Their feelings are put to the test and the guys and girls competing for the "Bachelor"/"Bachelorette" will also have things they are trying to figure out about each other. It's a mind-game more than anything since hearts are opened up, played with, closed off, and broken, and we really only understand why when we watch the season on TV.
6. Family Feud
Human Development and Family Studies (HDFS).
Each question that's asked on this show displays the minds and thoughts of the people who are surveyed when creating each episode of the show and it also shows how the competing family members think when the question is asked. Around family, some people act mature, others not so much, and there's always something interesting with each answer, especially the more perverted ones. Steve Harvey tries to keep the show appropriate though.
7 (and 8). American Idol (and The Voice)
Voice Performance.
This one is pretty straightforward since both "The Voice" and "American Idol" are focused on vocal performers and it's like your standard competition but there is public voting and it's broadcast on national television so millions are watching.
9. American Ninja Warrior
Exercise Science.
These competitors put so much work into the training room, especially since it's important to be fit for this show. Every muscle needs to be fine-tuned for competition, and being healthy is key too. An Exercise Science major is aware that the way we train will affect what muscles we target, and ideally we want to target all of them so we're keeping balance in the body as well as the diet.