test1review - Classification of Combinatorial problems i)...

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1 Classification of Combinatorial problems i) Order matters / does not matter Choose a committee of 3 out of 10 members (members are distinguishable): the order of the members in committee does not matter Choose president, vice-president and secretary out of 10 members: three different assignments mean the order is important C (10, 3) 3! 8 9 10 7! 3! 10! = = 10 9 8
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2 ii) identical objects Count different arrangements of 4 objects: AABC Modify the problem: AaBC Then we have 4!=24 distinguishable arrangements For any positions of B and C we have 2 choices, that should not be distinguished. So only 24/2=12 arrangements are distinct Count arrangements of AABB 12/2=6
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3 iii) with/without repetitions How many distinct 3-letter passwords exist? (order is important abc bac ) only once (without repetition) many times (with repetition) Any letter can be used 26 25 24 26 3 You draw 3 balls from a box with 10 red, 10 blue and 10green ( order is not important: rbg=brg=gbr=… ) *|*|* **||* ||***
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4 A committee of 3 is to be chosen from 5 Democrats,
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test1review - Classification of Combinatorial problems i)...

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