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MathematicsMathematics
23 June, 22:18

A survey of 180 college men was taken to determine participation in various campus activities. 43 were in fraternities, 52 participated in campus sports, 35 participated in various campus tutorial programs. 13 participated in fraternities and sports, 14 in sports and tutorial programs, 12 in fraternities and tutorial programs 5 participated in all 3 activities. 1. How many participated in only campus sports? 2. How many participated in fraternities and sports but not in tutorial programs? 3. How many participated in fraternities or sports but not in tutorial programs? 4. How many participated in exactly one of these activities? 5. How many participated in exactly 2 of these activities? 6. How many did not participate in any of these 3 activities?

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  1. 23 June, 22:30
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    It usually works best to draw the Venn diagram from the inside out, starting with the number in all three categories.

    1) 30 participated on campus sports only

    2) 8 participated in frats and sports but not tutorials

    3) 30 + 8 + 23 participated in frats or sports but not tutorials

    4) 30 + 14 + 23 = 67 participated in exactly one activity

    5) 9 + 7 + 8 = 24 participated in exactly 2 activities

    6) 180 - (67 + 24 + 5) = 84 participated in no activities
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