Permutations of Comics, Novels, and Magazines Without Restrictions

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In summary, there are three bundles of reading material, consisting of 4 comics, 2 novels, and 3 magazines, that can be placed together in 9! = 362880 ways with no restrictions. However, if the order of the comic books in each bundle does not change, the number of permutations would be \frac{9!}{4!} = 1782. The wording of the question is unclear and may affect the final answer.
  • #1
Bushy
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There are three separate bundles of reading material comprising of 4 comics, 2 novels and 3 magazines. They are placed together to form one pile.

In how many ways can this be done if there are no restrictions on where the individual items are to be placed?

I say 9! = 362880

Determine the number of permutations if the order of the comic books in each bundle does not change

I'm not sure what they mean by 'each bundle' here
 
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  • #2
This question is worded really strangely.

If you're arranging these into one pile and the order of the comic books doesn't change then I would say it's \(\displaystyle \frac{9!}{4!}\). Dividing by $4!$ accounts for all the different ways you can order the comic books but keep everything else the same. Since we want just one order I would say this is the answer but again this question is worded in a way where I'm not sure.
 
  • #3
Jameson said:
This question is worded really strangely.

I agree, the answer given is 1782, I've been trialing different answers to arrive there with no luck.
 

FAQ: Permutations of Comics, Novels, and Magazines Without Restrictions

What is a permutation?

A permutation is a mathematical concept that refers to the ways in which a set of objects can be arranged or ordered. It is a way of rearranging the elements of a set to create a new sequence or arrangement.

How is a permutation different from a combination?

A permutation takes into account the order of the elements in a set, while a combination does not. This means that in a permutation, the order of the elements matters, while in a combination, it does not.

How do you calculate the number of permutations?

The number of permutations can be calculated using the formula n!/(n-r)!, where n represents the total number of elements and r represents the number of elements being selected or arranged. For example, if you have 5 letters and want to arrange 3 of them, the number of permutations would be 5!/(5-3)! = 60.

Can a permutation have repeated elements?

Yes, a permutation can have repeated elements. In this case, it is called a repetition permutation. For example, the permutations of the word "book" would include "book," "obok," "kobo," and "okbo," among others.

How are permutations used in real life?

Permutations have various applications in fields such as mathematics, computer science, and statistics. They are used to calculate probabilities, analyze data, and solve problems related to combinations and arrangements. In real life, permutations can be used to organize data, schedule events, and create unique passwords, among other things.

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