Unformatted text preview: The four couple have 2! orderings within each pair, and then 4! orderings of the pairs giving a total of (2!) 4 Â· 4! = 384 , total orderings. Problem 11 (counting arrangements of books) Part (a): We have (3 + 2 + 1)! = 6! = 720 arrangements. Part (b): The mathematics books can be arranged in 2! ways and the novels in 3! ways. Then the block ordering of mathematics, novels, and chemistry books can be arranged in 3! ways resulting in (3!) Â· (2!) Â· (3!) = 72 , possible arrangements. Part (c): The number of ways to arrange the novels is given by 3! = 6 and the other three books can be arranged in 3! ways with the blocks of novels in any of the four positions in between giving 4 Â· (3!) Â· (3!) = 144 , possible arrangements....
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- Winter '08
- Probability, Order theory, Total order, possible arrangements