Statement 1 After drawing 3 masks, there can be 2 combinations possible -All three are of same color or two are of same color and 1 is of different color. Hence we can ensure that we can get two masks of same color after drawing 3 masks, randomly. If we draw less than 3 masks i.e. 2 masks, there is a possibility of both the masks being of different color hence we can't ensure that these masks can be of different color, hence the minimum number of masks we need to draw is 3. Statement 2 To calculate the minimum number of students required, we need to consider the worst case scenario i.e. the birthdays of students are evenly spread across all the 12 months. We'll have to assume that there are atleast 5 birthday is each month, so the total number of students required =5*12=60. To assure that there is 1 month in which we have 6 birthdays, we'll have to add 1 to this number, hence the minimum number of students required =60+1=61