Six students are running for the positions of president and vice-president, and five students are running for secretary and treasurer. If the two high

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Pzychoderek

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Six students are running for the positions of president and vice-president, and five students are running for secretary and treasurer. If the two highest vote getters in each of the two contests are elected, how many winning combinations can there be?
 
The highest vote getter can be selected from how many candidates?
The second highest vote getter can be selected from how many remaining candidates?
 
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Jomo said:
This problem can become complicated if the two lists of students have a non-empty intersection! I am leaning towards it couldn't be solved as stated.
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I'm inclined to say they are described as two separate contests, so it's reasonable to take it as saying that you can't run in both. Presumably, also, we don't need to worry about ties, as it only asks about the results, that is, the people elected to each of the four offices.
 
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