In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct? 1. At least 30 Indian participants are vegetarian. 2. At least 10 Indian participants are non-vegetarian. Select the correct answer using the codes given below:

Here's a brief explanation for each statement:

Statement 1: At least 30 Indian participants are vegetarian. Total participants = 100 Indians = 70 Vegetarians = 60

To find the minimum number of Indian vegetarians, we consider the maximum number of non-Indian vegetarians. Number of non-Indians = Total - Indians = 100 - 70 = 30. If all 30 non-Indians are vegetarian, then the remaining vegetarians must be Indian. Minimum Indian vegetarians = Total vegetarians - (Non-Indian vegetarians) = 60 - 30 = 30. Alternatively, using the principle of inclusion-exclusion: (Indians + Vegetarians) - Total = (70 + 60) - 100 = 130 - 100 = 30. This is the minimum overlap. So, Statement 1 is correct.

Statement 2: At least 10 Indian participants are non-vegetarian. Total participants = 100 Indians = 70 Non-vegetarians = Total - Vegetarians = 100 - 60 = 40.

To find the minimum number of Indian non-vegetarians, we consider the maximum number of non-Indian non-vegetarians. Number of non-Indians = 30. If all 30 non-Indians are non-vegetarian, then the remaining non-vegetarians must be Indian. Minimum Indian non-vegetarians = Total non-vegetarians - (Non-Indian non-vegetarians) = 40 - 30 = 10. So, Statement 2 is correct.

Since both statements are correct, the answer is C.