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Question Number 160389 by mr W last updated on 28/Nov/21

Commented by mr W last updated on 29/Nov/21

thanks for trying!  but it′s wrong sir. i think you   misunderstood the question. it is not  to select one pair from 20 people, but  to build 10 pairs from 20 people.  the two students from any college   should play against the students  from other colleges, not against each   other, so they should not be in a pair.

$${thanks}\:{for}\:{trying}! \\ $$$${but}\:{it}'{s}\:{wrong}\:{sir}.\:{i}\:{think}\:{you}\: \\ $$$${misunderstood}\:{the}\:{question}.\:{it}\:{is}\:{not} \\ $$$${to}\:{select}\:{one}\:{pair}\:{from}\:\mathrm{20}\:{people},\:{but} \\ $$$${to}\:{build}\:\mathrm{10}\:{pairs}\:{from}\:\mathrm{20}\:{people}. \\ $$$${the}\:{two}\:{students}\:{from}\:{any}\:{college}\: \\ $$$${should}\:{play}\:{against}\:{the}\:{students} \\ $$$${from}\:{other}\:{colleges},\:{not}\:{against}\:{each}\: \\ $$$${other},\:{so}\:{they}\:{should}\:{not}\:{be}\:{in}\:{a}\:{pair}. \\ $$

Commented by cortano last updated on 29/Nov/21

n(S)=C_2 ^(20) = 190  n(A)=190−10=180  P(A)=((180)/(190))=((18)/(19))

$$\mathrm{n}\left(\mathrm{S}\right)=\mathrm{C}_{\mathrm{2}} ^{\mathrm{20}} =\:\mathrm{190} \\ $$$$\mathrm{n}\left(\mathrm{A}\right)=\mathrm{190}−\mathrm{10}=\mathrm{180} \\ $$$$\mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{180}}{\mathrm{190}}=\frac{\mathrm{18}}{\mathrm{19}} \\ $$

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