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a) four members are running for president in a society with 50 members. how many different vote counts are possible, if each of the members vote for one of the four candidates?

b) four members are running for president in a society with 50 members. how many different vote counts are possible, if each of the members vote for one of the four candidates, or can choose to abstain?

 Jan 2, 2020
 #1
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(a) We want to distribute 50 votes among 4 categories.  The number of ways of doing this is \(\binom{49}{3} = 18424\)

 

(b) We want to distribute 50 votes among 5 categories, because we can think of abstaining as a category.  The number of ways of doing this is \(\binom{49}{4} = 211876\)

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 Jan 2, 2020
 #2
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I am not claiming to be positive but I think 

 

a) four members are running for president in a society with 50 members. how many different vote counts are possible, if each of the members vote for one of the four candidates?

50 stars, 3bars (to seperate into 4 bundles)        53C3 =23426

 Jan 2, 2020
edited by Melody  Jan 2, 2020
 #3
avatar+106933 
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b) four members are running for president in a society with 50 members. how many different vote counts are possible, if each of the members vote for one of the four candidates, or can choose to abstain?

 

Just count abstain as a 5th candidate.

 Jan 2, 2020
 #4
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so, 316251

Guest Jan 4, 2020

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