There are 10 white balls, 10 blue and 6 red balls in the urn. How many balls should

There are 10 white balls, 10 blue and 6 red balls in the urn. How many balls should be removed from the urn so that there are: 1) at least 2 balls of the same color; 2) exactly 2 red balls; 3) 7 balls of the same color.

1) In order to have two balls of the same color among the balls taken out, you need to remove 4 balls. Then even if the first three balls taken out were of different colors, then the fourth ball will match in color with one of them.

2) Since the balls are drawn randomly, it may happen that in the first attempts only white and blue balls are drawn. This means that in order to get two red balls for sure, you need to perform so many extractions to exceed the number of white and blue balls by two, that is, remove 10 + 10 + 2 = 22 balls.

3) In the longest case in terms of the number of balls being drawn, the balls will be removed alternating in color in such a way that on the 18 ball removed from the urn we have 6 white balls, 6 blue balls and 6 red balls. This means that you need to take out 19 more balls to get 7 balls of the same color.