What is the maximum number of girls who opted for Cooking Classes?
Number of those who opted for cooking which is more than the number of those who opted for exactly two of the three hobbies which in turn is more than those who opted for all three hobbies.
To maximize the number of girls who attend cooking classes, we only need to compare the girls who attend exactly two and who attend exactly three as all these will come under the individual subject.
So, assign 49 girls to all the three subjects and 51 girls in the exactly two. Also, 51 should be divided as equally as possible:
So, number of girls attending cooking class = 49 + 17 + 16 = 82.