Solutions from a student (dragged) 6

Solutions from a student (dragged) 6 - The four couple have...

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Giving seven possible locations for the A , B pair. Thus the total number of orderings is given by 2! · 6! · 7=10800 . Part (c): To place the men and women according to the given rules, the menandwomen must be interleaved. We have 4! ways to arrange the men and 4! ways to arrange the women. We can start our sequence of eight people with a woman o raman(g iv ingtwo possible choices). We thus have 2 · 4! · 4! = 1152 , possible arrangements. Part (d): Since the Fve men must sit next to each other their ordering canbespec iFedin 5! = 120 ways. This block of men can be placed in between any of the three women, or at the end of the block of women, who can be ordered in 3! ways. Since there are four positions we can place the block of men we have 5! · 4
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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 · 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!) · (2!) · (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 · (3!) · (3!) = 144 , possible arrangements....
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