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A certain club has  people, and  members are running for president. Each club member either votes for one of the  candidates, or can abstain from voting. How many different possible vote totals are there?

 Nov 7, 2022
 #1
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im deperate plesee

 Nov 7, 2022
 #2
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Hi are there any numbers that go with this post? because with none it's unsolvable.

 Nov 7, 2022
 #3
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Omg sorry here's the new question:

 

A certain club has 50 people, and 4 members are running for president. Each club member - including the members running for president - votes for one of the 4 candidates. Candidates may vote for themselves or for a different candidate. How many different possible vote totals are there?

 Nov 7, 2022
 #4
avatar+32 
+1

Hey actually this question was solved

 

here View question - help pls (0calc.com)

 

Go to the 6th answer it explains the best.

 Nov 7, 2022
 #5
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yes but it is wrong :(((

 Nov 7, 2022
 #6
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have you tried 4^50?

 Nov 7, 2022
 #7
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yes it is still wrong :((

 

i appreciate your help :)

 Nov 7, 2022
 #8
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can the people abstain from voting?

 Nov 7, 2022
 #9
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no they cannot abstain from voting

 Nov 7, 2022
 #10
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do you know combinations?

for this question you will use the combination formula which is

\(n!/r!(n-r)!\)

in this case your n is 50  and your r value is 4 because you have 50 options are you are choosing 4. 

When plugged into the formula this gives you 

\(50!/4!(50-4)!\)

simplified this is 

\(50!/4!(46)!\)

can you solve from here?

 Nov 7, 2022
 #11
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never mind I was given the wrong question to solve this one is slightly more complex but still doable haha

Logtoaster  Nov 7, 2022
 #12
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ok, the answer is either 1200 or 230300 (:

Hope I could help!

 Nov 7, 2022
 #13
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thank you i would have to ocouble check if that is right :)))

 Nov 7, 2022
 #14
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Two different questions are posted on this thread.   

 

Question 1:

A certain club has [50] people, and [4] members are running for president. Each club member either votes for one of the candidates, or can abstain from voting. How many different possible vote totals are there?

 

Question 2:

A certain club has 50 people, and 4 members are running for president. Each club member - including the members running for president - votes for one of the 4 candidates. Candidates may vote for themselves or for a different candidate. How many different possible vote totals are there?

 

Solutions Below....

 

GA

--. .- 

 Nov 7, 2022
 #15
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0

 

Solution for Q1:

(Because a member can abstain, this is counted as a vote for no candidate.)

 

Case one (1): All candidates receive at least one vote, including the no candidate, which means there is at least one abstention.

                     Partitions of 50 with a size of 5 = 2611

 

Case one (2): One candidate receives zero (0) votes; all others receive at least one vote.

                       Partitions of 50 with a size of 4 = 920

 

Case one (3): Two candidates receive zero (0) votes.

                      Partitions of 50 with a size of 3 = 208

 

Case one (4): Three candidates receive zero (0) votes.

                      Partitions of 50 with a size of 2 = 25

 

Case one (5): Four candidates receive zero (0) votes. This means everyone abstains, i.e. everyone votes for no candidate

                      Partitions of 50 with a size of 1 = 1

 

 

Total distribution of votes: 2611 + 920 + 208 + 25 + 1 = 3765

------------------

 

Solution for Q2:

 

(This is same as question 1, except the members cannot abstain.)

 

Case one (1): All candidates receive at least one vote

                      Partitions of 50 with a size of 4 = 920

 

 

Case one (2): One candidate receives zero (0) votes; all others receive at least one vote.

                       Partitions of 50 with a size of 3 = 208

 

 

Case one (3): Two candidates receive zero (0) votes.

                      Partitions of 50 with a size of 2 = 25

 

Case one (4): Three candidates receive zero (0) votes. One candidate receives all the votes.

                      Partitions of 50 with a size of 1 = 1

 

 

Total distribution of votes:  920 + 208 + 25 + 1 = 1154

 

 

 

GA

--. .- 

GingerAle  Nov 7, 2022
 #17
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I made a mistake,  here is the actual problem: A certain club has 50 people, and 10 members are running for president. Each club member either votes for one of the 10 candidates, or can abstain from voting. How many different possible vote totals are there?

Guest Nov 7, 2022
 #16
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Oh!  Here is the actual problem:  A certain club has 50 people, and 10 members are running for president. Each club member either votes for one of the 10 candidates, or can abstain from voting. How many different possible vote totals are there?

 Nov 7, 2022
 #18
avatar+2426 
0

The solution to this question is similar to those above, except you now have eleven (11) cases to analyze. 

 

  GA

--. .- 

GingerAle  Nov 7, 2022

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