perms restriction question (1 Viewer)

[yolo tengo]

hey everyone, im struggling in perms n combs so bad (its an universal experience atp) and mostly i'm struggling in the restriction part of this silly topic, can anyone help me w this question? 5b

 

[Chiprr]

It is cambridge y11 Ex14D Q5
View attachment 39247

My previous year 11 MX1 was a take-home task and I recognised the letters in two questions from the Cambridge textbook (we use In Focus). One didn’t have an answer or worked solution but the other was a worked example and so I got full marks for the question.

 

[Unovan]

For part a you have 8 total chairs so 8! total combinations of chairs. However there are only two types of chairs so you divide out the duplicates by dividing by the factorial of the amount of each duplicate. There's 5 of one kind and 3 of another so you divide by 5! * 3! giving you 8!/5!*3! final combinations.

For part b there are two green chairs on the end. This means that they don't change regardless of what combination the rest of the chairs are in. Hence you don't need to put them in your calculations. That means you can consider it as being 6 total chairs with 3 green and 3 red, giving you 6!/3!*3! total combinations.