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Suppose there are N male and N female students. They are randomly distributed into k groups.

Is it more probable for a male student to find himself in a group with more guys and for female student to find herself in a group with more girls?

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    My gut feeling is "no" because after picking one male student, you're choosing from N-1 male students and N female students. Not much difference, but it's there.2012-04-27
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    @El'endia Starman is not the majority of guys should be in the groups which have more guys and the majority of girls - in the groups with more girls?2012-04-27
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    Suppose there are three kinds of groups: those with more guys, those with more girls and those which have equal number. In the groups with equal number the number is equal, but among other groups, evidently those with majority of guys have more guys than those with the majority of girls.2012-04-27
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    Should not the groups with more guys have greater total number of guys than the groups with more girls?2012-04-27
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    for 2 boys and 2 girls, we can have the following distribution (bb,gg) (bg,bg)(bgg,b)(bggb)(bg,b,g)(b,b,g,g)(bb,g,g)(gg,b,b) so in this case only in 2 conformations i.e (bb,gg) and(bb,g,g) boys outnumber girls, hence the answer should be no2012-04-27
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    I meant the groups are equal in number.2012-04-27
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    Also I think these groups should be counted several times: (b1b2,g1g2), (b2b1,g1g2), (b1b2,g2g1) etc, which gives more combinations than for a distribution with smaller groups.2012-04-27
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    but the order of arranging them isnt our concern, so (b1b2,g1g2) are (b2b1,g1g2) both same. and also , in the question are all boys identical? or all girls identical?2012-04-27
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    Arranging is not our concern but we should ascribe different weights to each case. Anyway I was asking about a situation with even groups.2012-04-27

2 Answers 2