Question

counting question

Answer 1

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

Answer 2

i have found both 1 and 2 are true

Answer 3

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

Answer 4

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 ??!

Answer 5

of course 221 has only 2 prime factors was this a trick question

Answer 6

yes, especially if you have not memorized the larger primes (but computers come to the rescue!)

Answer 7

if one founds that the number of girls is 13 than it is easy to find 13C2=78

Answer 8

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)

Answer 9

thnks so much