You are the manager of your local softball team. Your first task of the day is to arrange the batting order for the next game. Because the players are so picky, you must justify your order using your mathematical skills and knowledge.
1. How many arrangements are possible?
2. What if the pitcher must be the first batter?
The team is composed of 4 women and 10 men. The league rules require at least 2 women participate in the game at any given time. All of the participants are able to play any of the positions.
3. Using the above information, how many batting orders are possible now?
4. Compare your solution in #3 with your solution in #1. Explain in sentence form why the solutions are the same or different.