mathmath333
  • mathmath333
counting question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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mathmath333
  • mathmath333
In a carrom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl. Consider the following statements : statement 1.) The total number of students that participated in the competition is 30 statement 2.)The number of games in which both players were girls is 78 Which of the statements given above is/are correct? a.)1 only b.)2 only c.)Both 1 and 2 d.)Neither 1 nor 2
mathmath333
  • mathmath333
i have found both 1 and 2 are true
mathmath333
  • mathmath333
soln is 1.) 17 boys* 13 girls=221 2.) 13C2=78 but i am confused how did one arrive at this thinking with many possiblities

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phi
  • phi
I am thinking first boy plays against n girls, 2nd boy plays against n girls, etc we get mn games with 1 boy vs 1 girl thus mn= 221 this suggests we factor 221 guess what it factors into ??!
mathmath333
  • mathmath333
of course 221 has only 2 prime factors was this a trick question
phi
  • phi
yes, especially if you have not memorized the larger primes (but computers come to the rescue!)
mathmath333
  • mathmath333
if one founds that the number of girls is 13 than it is easy to find 13C2=78
phi
  • phi
yes, to solve this problem , you have to find that trick, i.e. figure out m*n= 221 and then notice that only 17 and 13 are factors of 221 (other than 1 and 221, and this one is excluded because both m and n > 1)
mathmath333
  • mathmath333
thnks so much

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