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: 1. The total number of students that participated in the competition is 30. 2. The number of games in which both players were girls is 78. Which of the statements given above is/are correct?

Here's a brief explanation: 1. **Identify the given information:** * Number of boys = m * Number of girls = n * Condition: m > n > 1 * Number of games between a boy and a girl = 221 2. **Formulate the equation:** The number of games played between one boy and one girl is given by the product m * n. So, m * n = 221. 3. **Find m and n:** We need to find two factors of 221 such that m > n > 1. Factoring 221: 221 = 13 * 17. Given m > n, we have m = 17 and n = 13. This satisfies m > n > 1 (17 > 13 > 1). 4. **Evaluate Statement 1:** "The total number of students that participated in the competition is 30." Total students = m + n = 17 + 13 = 30. Statement 1 is correct. 5. **Evaluate Statement 2:** "The number of games in which both players were girls is 78." The number of games between two girls is given by the combination formula C(n, 2). C(n, 2) = C(13, 2) = (13 * (13-1)) / 2 = (13 * 12) / 2 = 13 * 6 = 78. Statement 2 is correct. Since both statements 1 and 2 are correct, the answer is C. The final answer is C