Permutation of subsets with like objects Question

In summary, the question involves finding the number of permutations for a subset of 3 objects from a superset of 8 objects where 5 are identical. The solution provided by the person asking the question is mostly correct, except for the factor of C(5,2), which should be 1 instead of 10. After receiving feedback, they have revised their answer to be 106, rather than 196. They have also shared their work and asked for confirmation.
  • #1
Astro
48
1
Permutations of subsets with like objects Question

Hello, I'd like to know if I solved the question correctly; if not, I'd appreciate some help.

Question:
Calculate the number of permutations for a subset of 3 objects from a superset of 8 objects where 5 are alike.

My solution attempt: (Please see attachment).
 

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  • #2
Your solution is fine except for the factors like C(5,2). This looks like you are counting the ways of picking 2 objects from 5 identical objects. That's not C(5,2). It's 1.
 
  • #3
Thank you, you're input helped! I believe the answer is 106, not 196. I was going to post a detailed and neat explanation of how I got 196 but I'm so busy that I can't (which is why it took so long for me to reply); however, since I asked for help and you were nice enough try, the least I can do is post my rough work for you and others to see. I'm pretty sure I got it right this time; if not, someone, let me know.
:smile:
 

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FAQ: Permutation of subsets with like objects Question

What is the definition of "Permutation of subsets with like objects"?

Permutation of subsets with like objects refers to the arrangement of a set of items where some items are identical, resulting in multiple identical subsets. This is different from traditional permutation where all items are unique.

How is "Permutation of subsets with like objects" different from traditional permutation?

Traditional permutation involves arranging a set of unique items in a specific order, while permutation of subsets with like objects involves arranging a set of items that may have identical elements. This results in multiple identical subsets with different arrangements.

What is the formula for calculating the number of permutations in "Permutation of subsets with like objects"?

The formula for calculating the number of permutations in permutation of subsets with like objects is n! / (n1! * n2! * ... * nk!), where n is the total number of items and n1, n2, etc. represent the number of identical elements in the set.

Can the number of permutations in "Permutation of subsets with like objects" exceed the number of items in the set?

Yes, the number of permutations in permutation of subsets with like objects can exceed the number of items in the set. This is because the formula takes into account the number of identical elements in the set, resulting in a larger number of possible arrangements.

What are some real-life applications of "Permutation of subsets with like objects"?

Permutation of subsets with like objects can be applied in various fields such as genetics, inventory management, and statistics. For example, in genetics, this concept can be used to calculate the different combinations of genes in a population. In inventory management, it can be used to determine the number of unique product combinations with varying quantities. In statistics, it can be used to calculate the number of different outcomes in a survey with multiple choice questions.

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