Hi there,I need some help with my stats homework. I am really struggyling with stats and need some advice on how to improve.There are 15 students, 15 chairs, 4 wear glasses, 7 wear hoodies.How many ways can you sit on these chairs: 1. so that Richard and David do not move2. so that Robert and Hannah stay sitting next to each other3. so that the students wearing glasses sit next to each other 4. so that Joe and Megan are sitting 'at the ends'5. so that the students wearing hoodies do not sit next to each other and those without do not sit next to each other 6. so that James does not sit next to Ben.*Apparently the hardest question. so that the students wearing glasses do not sit next to each other.
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- 13-10-2016 18:12
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- 13-10-2016 19:12
I'm not an expert on S1 but this how I think it works...
1. For this part, you know that Richard and David must sit where they currently are sitting. This means then that those two seats are taken so there are only 13 seats left. Since the order in which they are sitting matters it is a permutation, meaning that the total arrangements of people on the remaining seats is 13 Factorial (!).
2. Robert and Hannah stay sitting next two each other, can be thought of as their two chairs being joined together, this means that there are now effectivley 14 chairs, so there would be 14! ways of sitting on those chairs. However, Robert and Hannah can sit on the 'joined chair' in two possible ways (Robert, Hannah or Hannah, Robert). This means then that the 14! arrangement must be multiplied by a further 2 arrangements.
3. If you look at this question the same ways as question 2, you should get the right answer, just remember that there are now 4 chairs joined so an additional 4! arrangements to multiply at the end.
4. Let Joe and Megan sit at the end then you are left with 13 seats, work out the number of ways those remaining 13 seats are filled and multiply by the number of ways Joe and Megan can sit at the ends.
I'm not too sure about 5.
6. Find the total number of arrangements of all the seats, then subtract the ways in which James and Ben DO sit together. This will leaves the number of ways they don't.
In my opinion this is the hardest part about S1, and I think the only thing that makes it easier is to just practise loads of these types of questions. Also, drawring diagrams and thinking logically about each question helps.