Isn't the question 'what is the total possible number of combinations possible when six candidates split up 12,342 votes?'

If only two candidates were running and 12,002 votes were cast, the probability of any particular set of totals would be 1/12,002, wouldn't it?

12,002 to 0
12,001 to 1
.....
1 to 12,001
0 to 12,002

Like playing cards. The probability of drawing any arbitrary hand is about 2,600,000:1

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