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A shelf has 12 books. How many ways are there to choose 5 books so that no two adjacent books are chosen?
Hint: represent the books that are chosen by bars and the books not chosen by stars. Count the number of sequences of five bars and seven stars so that no two bars are adjacent.
| * | * | * | * | * | * | * |
the q is equivalent to choosing 5 out of 8 possible non-adjacent bars
there are 8c5 = 8!/5!3! = 56 ways <--------
Target 5 Shelf Bookcase Review