S1: combinations/permutations question - HELP PLEASE
Hello.
I find stats pretty easy but I always struggle with perms and combinations.
I know the answers to these questions but I don't understand the rationale behind them. Would someone be so kind as to explain these questions for me? Thank you!
"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.
(i) Calculate the number of ways in which Peter may choose his three-course meal.
(ii) 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."
I find stats pretty easy but I always struggle with perms and combinations.
I know the answers to these questions but I don't understand the rationale behind them. Would someone be so kind as to explain these questions for me? Thank you!
"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.
(i) Calculate the number of ways in which Peter may choose his three-course meal.
(ii) 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."
Original post by outbriefcandle-
Hello.
I find stats pretty easy but I always struggle with perms and combinations.
I know the answers to these questions but I don't understand the rationale behind them. Would someone be so kind as to explain these questions for me? Thank you!
"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.
(i) Calculate the number of ways in which Peter may choose his three-course meal.
(ii) 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."
I find stats pretty easy but I always struggle with perms and combinations.
I know the answers to these questions but I don't understand the rationale behind them. Would someone be so kind as to explain these questions for me? Thank you!
"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.
(i) Calculate the number of ways in which Peter may choose his three-course meal.
(ii) 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."
(i) This is simply 4x5x3 = 60. Imagine a tree diagram with each possible combination... how many branches will there be?
(ii-A) You are trying to calculate the number of combinations of 2 starters, where they are both different. There are 4 possible starters, hence you want the number of ways to pick 2 from 4, which is nCr (number of ways to pick r items from n objects). Hence 4C2, which is 6.
(ii-B) Similarly to part (ii-A), except you need to do the same for the main course and dessert. There are 5 mains, and you want 2, hence 5C2 = 10. There are 3 sweets, and you want 2, hence 3C2 = 3. Multiply these two numbers together along with the answer to (ii-A): 6x10x3 = 180.
Hope this helps!
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