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#1 2006-12-20 03:38:17

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

The Six Journalists

Six journalists are to vote for their favourite sports person from a list of 5 candidates. In how many different ways can the group of journalists vote?
I got:
[6][5] = 6 × 5 = 30 ways.
The answers displayed:
5^6 = 15625 ways, which I find a little random and hard to believe.
Who is correct? Help plz
Thanks

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#2 2006-12-20 04:55:43

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: The Six Journalists

well lets explain the answer

if you have 1 jouranlist, there are 5 ways he can vote

if you have 2 journalists, there are 5 ways each can vote, and for each of the 5 ways the first can vote, the other can vote one of 5 ways, so you have 5x5 combinations because for each of the 5 ways the first can vote, there are 5 ways the second can vote.

if you have 6 -> 5^6 combinations.

Last edited by luca-deltodesco (2006-12-20 04:56:45)


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#3 2006-12-20 04:56:45

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: The Six Journalists

The displayed answer is right.

One journalist has 5 different candidates to choose from, so they have 5 choices.
Between them, two journalists have 25 different combinations of choices, because the first journalist could pick option 1 and then the second would have 5 choices, but then then first journalist could pick option 2 and the second would have 5 different choices, and so on.

It follows that 3 journalists will have 125 choices, 4 journalists will have 625 choices, and so on, with the number of choices multiplying by 5 each time a new journalist is introduced.

Therefore, with 6 journalists, there are 15625 different ways.

Edit: Bah, luca got there before me. But then if you consider his edit, we posted the right answer at exactly the same time! cool


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#4 2006-12-20 05:32:28

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: The Six Journalists

Yes, but if the journalists all have the same name, then the number of ways might be less, probably the factorial formula instead of power.


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#5 2006-12-20 08:15:13

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: The Six Journalists

well no, because the question asks how many different ways can 6 unique people vote

if you have the first 4 voting for andrew, and the last 2 voting for frank, if you then have the first 2 with frank, and last 4 with andrew, its still a unique way of voting, because its different people voting for different candidates, relentless of whether the total number of votes for each candidate is the same.


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#6 2006-12-20 10:58:30

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: The Six Journalists

Ah yes thanks everyone, I was thinking in the wrong terms

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