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 05-21-2012, 04:41 PM #1 Senior Member     Status: Pre-Dental Join Date: Jun 2011 Posts: 467 Math Destroyer Test 1 #40 SDN Members don't see this ad. (About Ads) In how many ways can 4 of the same (identical) physics books, 3 of the same algebra books, and 2 of the same chemistry books be arranged on a shelf? Answer: 1260 I am not quite understanding this one...any help would be appreciated! Thanks!
 05-21-2012, 04:58 PM #2 Senior Member     Status: Dental Student Join Date: Mar 2012 Location: Gainesville, FL Posts: 178 You have 9 books total right? And presumably 9 spots on the book shelf. If all of the books were different, we'd just do 9 factorial. But since we have replicas of the same books, we're going to get duplicate combinations. To account for duplicates items in a set, we divide by the factorial of the number of duplicates. For example, 4 duplicate physics books means we divide by 4 factorial, and 3 duplicate algebra books means we divide by 3 factorial. When all is said and done, you'll have 9! / (4!*3!*2!). 9 for the original amOunt of books, and divide by the factorials of the duplicates to account for the duplicate sets from ordering them on the book shelf.

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