please explain all the steps

7) Congratulations, you are getting married! You are working with the caterer, to set up the buffet. You are allowed to pick so many choices for each part of the buffet spread. Here is the list of what you can choose from. Notice how many you can choose from each part of the menu. Appetizers Salads Entrees Sides Desserts Pick 3 Pick 4 Pick 3 Pick 4 Pick 6 Artichoke Dip Caesar Chicken Cordon Bleu Mashed Potatoes Blueberry Cheesecake Swedish Meatballs Mixed Green Pork Tenderloin Wild Rice Strawberry Shortcake Buffalo Wings Spinach and Egg Roast Beef Steamed Vegetables Chocolate Cake Spring Rolls Berries and Nuts Stewed Tofu Frites Carrot Cake Calamari Fruit Lobster Scalloped Potatoes Tuxedo Cake Bruschetta Bites Greek Black Beans Lemon Squares 7-Layer Dip Pasta Perogies Nanaimo Bars Cool Cucumber Assorted Cupcakes Broccoli Apple Pie Tiramisu a) Give one possible buffet list below: Appetizers Salads Entrees Sides Desserts b) What is the total number of buffets possible given the options above? We need to take the number of choices at each stage, and then multiply the stages together: c) What is your favourite single item on the menu above?5) Your baseball team enters a best out of 7 series. How many different ways can you win in exactly 6 games? In order to win the series in exactly 6 games, we have to win exactly 3 and lose exactly 2 of the fi 5 games, and win the 6th one: W Since the 6th game is determined for us, we are really just figuring out how we can win exactly 3 the first 5 games. We can think about it two ways: First we can think about all the different arrangements of these letters: W WW LL So in that case it is just like question 4: 6) This same baseball team is made up 7 girls and 8 boys. There are 9 people on the field at a time in a baseball game. If at least 4 of the people on the field have to be girls, how many different possible ways can your team take the field? If at least 4 can be girls, then we can have 4 girls 5 boys, or 5 girls 4 boys, or 6 girls 3 boys, or 7 girls 2 boys. Since we only have 7 girls to choose from, 8 girls 1 boy is not an option. Hint: Write out all the options using combinations and multiply each of them by 9