D1 Aqa help needed Watch

Hjyu1
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I understand that iii) is (n-1)! Because it is directed tours.

However I don't get why iv) is n!

Can anyone help me please!
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ghostwalker
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(Original post by Hjyu1)
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I understand that iii) is (n-1)! Because it is directed tours.

However I don't get why iv) is n!

Can anyone help me please!
Grand Hotel is not a museum. Excluding that, there are n museums to visit. There are n! orderings of n items, hence that number of tours.
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Hjyu1
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(Original post by ghostwalker)
Grand Hotel is not a museum. Excluding that, there are n museums to visit. There are n! orderings of n items, hence that number of tours.
Is my thinking right here there is (n-1)! But n times so it's n!
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ghostwalker
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(Original post by Hjyu1)
Is my thinking right here there is (n-1)! But n times so it's n!
I don't know where your (n-1)! has come from,

or why you think the answer to iii) is (n-1)! since that doens't involve n.

Need some explanation of your thinking.
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Hjyu1
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(Original post by ghostwalker)
I don't know where your (n-1)! has come from,

or why you think the answer to iii) is (n-1)! since that doens't involve n.

Need some explanation of your thinking.
In the book I learnt this from it said that in a directed network there are (n-1)! Tours and n! Calculations so I tried go off that( for n vertices ) and for iii I subbed in the values in to the equation so n=4 to get 3!
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ghostwalker
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(Original post by Hjyu1)
In the book I learnt this from it said that in a directed network there are (n-1)! Tours and n! Calculations so I tried go off that( for n vertices ) and for iii I subbed in the values in to the equation so n=4 to get 3!
OK, the n they are using there is the total number of vertices.

So for part iii) there are 4 vertices, hence 3! tours. Or looking at it another way, there are 3 museums to visit in any order before returning to the hotel. 3 things can be ordered in 3! ways.

For iv) there are n+1 vertices (n museums and the hotel), and hence (n+1 - 1)! tours, i.e. n! tours. Or again just considering the museums, starting at the hotel, we visit n museums in any order - there are n! possible orders - and return to the hotel.

Either way, it's not a good idea to just learn something rote from the book - you need to understand why it is what it is, and then you will be able to adapt it to similar situations.
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Hjyu1
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(Original post by ghostwalker)
OK, the n they are using there is the total number of vertices.

So for part iii) there are 4 vertices, hence 3! tours. Or looking at it another way, there are 3 museums to visit in any order before returning to the hotel. 3 things can be ordered in 3! ways.

For iv) there are n+1 vertices (n museums and the hotel), and hence (n+1 - 1)! tours, i.e. n! tours. Or again just considering the museums, starting at the hotel, we visit n museums in any order - there are n! possible orders - and return to the hotel.

Either way, it's not a good idea to just learn something rote from the book - you need to understand why it is what it is, and then you will be able to adapt it to similar situations.
Yeah I normally try get an understanding of it properly however I only just got entered for the exam so I had to learn it quickly and d1 is suppose repetitive and I'm aiming for 80-90 % but yeah thanks for the help I get it now
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ghostwalker
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(Original post by Hjyu1)
Yeah I normally try get an understanding of it properly however I only just got entered for the exam so I had to learn it quickly and d1 is suppose repetitive and I'm aiming for 80-90 % but yeah thanks for the help I get it now
Cool. Sorry to hear you got entered with short notice. Good luck with your exam.
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