4 Peter and Esther visit a restaurant for a three-course meal. On the menu there are 4 starters, 5 main courses and 3 sweets. Peter and Esther each order a starter, a main course and a sweet.
- Calculate the number of ways in which Peter may choose his three-course meal.
- Suppose that Peter and Esther choose different dishes from each other.
(A) Show that the number of possible combinations of starters is 6 .
(B) Calculate the number of possible combinations of 6 dishes for both meals. - Suppose instead that Peter and Esther choose their dishes independently.
(A) Write down the probability that they choose the same main course.
(B) Find the probability that they choose different dishes from each other for every course.