A survey of 180 college men was taken. 43 students were in fraternities, 52 participated in campus sports, and 35 participated in campus tutorial programs. 13 participated in fraternities and sports, 14 in sports and tutorial programs, and 12 in fraternities and tutorial programs. 5 participated in all three activities. To start
D) How many participated in fraternities and sports but not in tutorial programs?
E) How many participated in only sports?
Steve answered this a few hours ago.
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To find the number of participants who were in fraternities and sports but not in tutorial programs, we can use the principle of inclusion-exclusion.
1. Start by finding the total number of participants in fraternities and sports, which is given by the intersection of the two sets:
Fraternities and sports = 13 participants
2. Subtract the number of participants who were in all three activities since they are already counted in the previous step:
Fraternities, sports, and tutorial programs = 5 participants
3. Finally, subtract the number of participants who were in all three activities from the total number of participants in fraternities and sports:
Fraternities and sports but not in tutorial programs = 13 - 5 = 8 participants.
Therefore, 8 participants participated in fraternities and sports but not in tutorial programs.
To find the number of participants who participated in only sports, you can use the following steps:
1. Start by finding the total number of participants in sports, which is 52.
2. Subtract the number of participants who were in fraternities and sports, as they are already counted in the previous step:
Fraternities and sports = 13 participants
3. Subtract the number of participants who were in all three activities since they are already counted in the previous step:
Fraternities, sports, and tutorial programs = 5 participants
4. Finally, subtract the number of participants who were in fraternities and sports and those who were in all three activities from the total number of participants in sports:
Only sports = 52 - 13 - 5 = 34 participants.
Therefore, 34 participants participated in only sports.