Combinatorics problem - Permutations of ABDEFGH

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SUMMARY

The discussion focuses on calculating the number of permutations of the letters ABCDEFGH that include the specific strings BA and FGH as clusters. The correct approach involves treating these clusters as single objects, resulting in a total of 5 objects: BA, C, D, E, and FGH. The calculation yields 5! = 120 permutations. The method remains valid regardless of the alphabetical order of the clusters, confirming the accuracy of the solution presented.

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Goldenwind
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In theory I'm done this question, but would like to get it checked.

22) How many permutations of the letters ABCDEFGH contain
c) the strings BA and FGH?

Answer:

5 objects: BA, C, D, E, FGH.
Total: 5! = 120

This is following the example in the book. However, the example only has one cluster (Where a cluster is like BA, or FGH), and all of the book's clusters are in alphabetical order.

For something like this, where we have two clusters, and it's BA, not AB, does my method still work?
 
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That the order is alphabetical makes absolutely no difference. You knew that in your heart, right?
 
That's what I figured, hence how I got my answer, but just wanted to check to be sure.
 

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