Discrete Mathematics

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Students at Apollo Elementary School receive ribbons at the end of each year at a school-wide awards ceremony. This year 120 students receive gold stars for perfect attendance, 180 receive certificates for participating in the science fair, and 80 students receive blue ribbons for outstanding grades. Of these, 40 students who receive the attendance star receive no other award, 50 students who receive the science fair certificate receive no other award. In addition, 10 students receive all three awards and 65 students receive no awards. Draw a Venn Diagram for this situation, and determine how many students attend the school this year.

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