17. In a photo lab, there are 130 photographs, of which 35 are from the fourth grade, 30 from the fifth, 25 from the sixth, 20 from the seventh, and the rest are from grades 1-III. The photographs are mixed and cannot be distinguished by touch. What is the smallest number of photographs that need to be taken, without seeing them, to ensure that among them there are at least 15 from one of the grades IV-VII?
17. Let's consider the most "unfavorable" case: we take all the photographs of classes I-III $(130-(35+30+25+20)=20)$, then it may turn out that 14 photographs were taken from each of the IV-VII classes, making a total of $14 \cdot 4+20=76$ photographs. Now, if we take one more, then one of the IV-VII classes will have 15. Therefore, we need to take 77 photographs.