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Dolores has a collection of eight books, including “The Great Gatsby” and “The South Beach Diet”. How many ways can she arrange three of her books on a bookshelf, where “The Great Gatsby” and “The South Beach Diet” are not next to each other? Note: Any arrangement where either “The Great Gatsby” or “The South Beach Diet” do not appear is acceptable.

 Mar 27, 2021
 #1
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You do realize that reposting doesn't increase your chances of getting an answer, right? It only annoys the moderators. 

 Mar 27, 2021
 #2
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By inclusion-exclusion, the number of ways is 10*9*8 - 9*8 - 9*8 + 8 = 584.

 Mar 27, 2021
 #3
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8 books choose 3 = 336   ways 

    4 ways   the two books COULD be  together in a group of 3   with six choices for the third book = 4 *6

        336 - 4*6 = 312 ways

 Mar 27, 2021
 #4
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Im not sure- Im feeling dumb today :')

wolfiechan  Mar 27, 2021

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