Arnold F. answered • 01/13/16
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a) The books by Conrad are arranged as a single unit.
First calculate the number of permutations of just the Conrad books (as a unit): 3!
Now since there are 6 other books and the Conrads are now one unit there are 7! ways of that arrangement.
The final step is to multiply 3! x 7!
try b and c and let me know how far you get.
Arnold F.
For part b to keep the Dickens books separate since there are so many ways that can happen let's do it differently.
Calculate the total number of ways to arrange the books without any restrictions at all: 9! and then subtract the number of ways that are in that number that violate the condition i.e. that the books are together. But that technique was what I did in part (a) for the Conrad books: 8!*2!.
That makes the part(b) answer 9! - 8!2!.
Try part (c) and let me know how what you are trying. What grade class is this for?
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01/14/16
Daniel K.
Im in Year 10. I cant do part (c). Can u help me?
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01/14/16
Arnold F.
OK. This one is more complicated than part (b). Since there are 3 books and we don't want any 2 of them next to each other the techniques of part (b) won't completely work.
By that I mean if we do 9! - 7!3! all we are doing is subtracting the permutations that have all 3 Conrad books together.
So I am going to do this one slightly differently.
If we arrange the six other books (6!) first we have 7 positions in which to insert the Conrad books:
SASBSCSDSESFS the other six books are A-F and S represents a possible space for a Conrad book.
Since there are seven positions we are selecting 3 of them to insert the Conrad books. That means there will be 7P3
ways of doing that. So this answer should be 6! (7P3).
This techniques could also have been used in part (b).
Daniel,
These kinds of techniques are better explained more in depth than I can do here. If you have questions like this in the future I would suggest you discuss with your parents the possibility of one-on-one lessons. I teach classes involving this topic and many other topics in finite math. If you have any other questions feel free to click on my profile and send me a direct message.
Arnold
There might be an easier way but here is one technique:
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01/14/16
Erick L.
How do you know it's sasasosislas.... ?
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09/13/20
Erick L.
Is it random or ?
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09/13/20
Fflame T.
Thank you
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03/13/21
Daniel K.
01/13/16