Assignment:
Q1. A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different meals consisting of one salad, one main dish, and one dessert are possible?
Q2. A group of 3 students is to be selected from a group of 12 students to take part in a class in cell biology.
a. In how many ways can this be done?
b. In how many ways can the group who will not take part be chosen?
Q3. Pizza Varieties A television commercial for Little Caesars pizza announced that with the purchase of two pizzas, one could receive free any combination of up to five toppings on each pizza. The commercial shows a young child waiting in line at Little Caesars who calculates that there are 1,048,576 possibilities for the toppings on the two pizzas.*
a. Verify the child’s calculation. Use the fact that Little Caesars has 11 toppings to choose from. Assume that the order of the two pizzas matters; that is, if the first pizza has combination 1 and the second pizza has combination 2, that is different from combination 2 on the first pizza and combination 1 on the second.
Q4. After studying all night for a final exam, a bleary-eyed student randomly grabs 2 socks from a drawer containing 9 black, 6 brown, and 2 blue socks, all mixed together. What is the probability that she grabs a matched pair?
Q5. Suppose that a family has 5 children. Also, suppose that the probability of having a girl is 1/2. Find the probabilities that the family has the following children.
Q6. A coin is tossed 6 times. Find the probabilities of getting the following
Provide complete and step by step solution for the question and show calculations and use formulas.