math datqvault Q 2:#35

[Menthol]

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Alex, who has four books, and Susan, who has three books, want to arrange their books on a shelf. If Susan has two books in common with Alex, how many distinct arrangements can they make using all seven of the books?

eq for this question is 7!/ (2! 2!)
i know it has to do w/ two books in common i dont know why i need to divide 7! by 2!2!
thank you

 

[theleatherwalle]

google permutation and combination. it will explain everything.

 

[torobcheh21]

i thought it has to do with how many unique books each person has...can anyone confirm this?

 

[NDPitch]

This is explained well in Destroyer. If they didn't have any books in common, it's simply 7! - but when you have duplicates you have to divide by the number of choices in common, factorial. This is because you've over counted. If you think about it, it does make sense. Say you have 7 books, but 3 of them are the same book. How many ways can you arrange them on a shelf?

You'd think 7! at first, but if you think more, you'll see that there are quite a number of equivalent permutations of the books. If you had an arrangement on the shelf, and then swapped the places of some of the identical books, you'd still have the same arrangement. Thus, you have to do 7!/3! in this example.