two
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252 teams.
Any 3 from 6 is 6!/(3! x 3!) ie 720/36 which is 20: ABC/ABD/ABE/ABF/ACD/ACE/ACF/ADE/ADF/AEF/ BCD/BCE/BCF/BDE/BDF/BEF/CDE/CDF/CEF/DEF. If the order in which they can run is taken into account then that 20 must be multiplied by 6 viz: ABC/ACB/BAC/BCA/CAB/CBA etc
18
Five groups of five people. Simple math my dear.
I figured out the answer: 18+7 = 25, So 25C5 = 53,130 Teams. This assumes there are no sex restrictions on the teams (for example, "teams must include at least one boy and at least one girl"). That would be a lot more complicated, and if that's a factor you'd need to specify exactly what the restrictions are.