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[Core] 高手入黎,唔識做permutation同combination

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高手入黎,唔識做permutation同combination

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1
Peter plans to deliver 12 packages to 12 different spots
a) 3 packages will be delivered to 3 spots in the same district, so they will be delivered successively. How many delivery sequences does he have now? (Ans: 21 772 800)
b) Apart from the 3 packages mentioned in (b), there are 4 packages to be delivered to 4 spots in another district successively. How many delivery sequences does he have now? (Ans: 725 760)


2
A group of seven people queue up to enter into a museum. It is given that Cherry and Rainbow are two of them.
a) If Cherry cannot be the first one and Rainbow cannot be the last one, how many arrangements are there? (Ans:3720)


3
There are 12 differentplants in the balcony, and 5 of them are cactuses. The plants are now arrangedin a row
a.
If any two cactuses cannot be placed next to each other, how many permutation are there?(Ans: 33 868 800)
b.
If only 3 of the cactuses are placed next to each other, how many permutation are there? (Ans: 101 606400)
c.
If cactuses must be placedat the two ends, how many permutation are there? (Ans: 72 576 000)
d.
If cactuses cannot be placed at the two ends, how many permutation are there? (Ans: 152 409 600)
e.
If cactuses cannot be place at both ends at the same time, how many permutation are there? (Ans: 406 425600)


4
There are 9 different books
c) How many ways to group the books into 3 piles such that there are 3 books in each pile? (Ans: 280)
   

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4. 9C3*6C3 / 3P3 = 280

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3
a 7P7* 8P5
b 7P7* 8P3 * 3P3
c 5P2 * 10P10
d 7P2 * 10P10
e 12P12 - 5P2* 10 P10

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2. a  1*6P6 + 5*5*5P5

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咁簡單都唔識?第時返工冇人教你架喎咁係咪唔做?

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回覆 4# 數痴夢王 的帖子

thank you so much!!

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1. (a) 10P10 * 3P3
   (b) 7P7 * 3P3 * 4P4

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