Arun sharma

Question

In a carrom board game competition, m boys 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:
I. The total number of students that participated in the competition is 30.
II. The number of games in which both players were girls is 78.
Which of the statements given above is/are correct?
(a) I only (b) II only
(c) Both I and II (d) Neither I nor II.

Answer 1

both 1 and 2..

221 matches played between boys and girls..

suppose m boys and n girls are there, therfore total matches between boys and girls will be m*n,

m*n= 221...and there are only two factors of 221(17,13)...

therefore m=17 and n=13(because no. of boys are greater than no. of girls).

now,

no. of matches played between girls only will be C(n,2)=C(13,2)=78...

Comments

Awsome explanation.