In a survey of 280 college students, it is found that
67 like brussels sprouts,
93 like broccoli,
60 like cauliflower,
26 like both brussels sprouts and broccoli,
21 like both brussels sprouts and cauliflower,
20 like both broccoli and cauliflower, and
10 of the students like all three vegetables.
How many of the 280 college students do not like any of these three vegetables?
To find the number of students who do not like any of these three vegetables, we need to subtract the total number of students who like at least one of the vegetables from the total number of students.
Let's break down the information given:
- Students who like brussels sprouts: 67.
- Students who like broccoli: 93.
- Students who like cauliflower: 60.
- Students who like both brussels sprouts and broccoli: 26.
- Students who like both brussels sprouts and cauliflower: 21.
- Students who like both broccoli and cauliflower: 20.
- Students who like all three vegetables: 10.
To find the total number of students who like at least one vegetable, we can add the students who like each vegetable separately and subtract the students who like more than one vegetable once (to avoid double counting).
Total number of students who like at least one vegetable = (Students who like brussels sprouts) + (Students who like broccoli) + (Students who like cauliflower) - (Students who like both brussels sprouts and broccoli) - (Students who like both brussels sprouts and cauliflower) - (Students who like both broccoli and cauliflower) + (Students who like all three vegetables)
Total number of students who like at least one vegetable = 67 + 93 + 60 - 26 - 21 - 20 + 10
= 163
Now, to find the number of students who do not like any of the three vegetables, we subtract the total number of students who like at least one vegetable from the total number of students:
Number of students who do not like any vegetable = Total number of students - Total number of students who like at least one vegetable
= 280 - 163
= 117
Therefore, 117 college students do not like any of these three vegetables.
To find the number of college students who do not like any of the three vegetables, we need to subtract the total number of students who like at least one of the vegetables from the total number of students, which is 280.
To calculate this, we first need to determine the number of students who like at least one vegetable. We can do this by summing the number of students who like each vegetable individually, subtracting the number of students who like two vegetables, and finally adding the number of students who like all three vegetables.
Let's calculate step by step:
1. Number of students who like brussels sprouts = 67
2. Number of students who like broccoli = 93
3. Number of students who like cauliflower = 60
To find the number of students who like two vegetables:
a. Number of students who like both brussels sprouts and broccoli = 26
b. Number of students who like both brussels sprouts and cauliflower = 21
c. Number of students who like both broccoli and cauliflower = 20
To find the number of students who like all three vegetables:
Number of students who like all three vegetables = 10
Now, let's calculate the total number of students who like at least one vegetable:
Total = (Number of students who like brussels sprouts) + (Number of students who like broccoli) + (Number of students who like cauliflower) - [(Number of students who like both brussels sprouts and broccoli) + (Number of students who like both brussels sprouts and cauliflower) + (Number of students who like both broccoli and cauliflower)] + (Number of students who like all three vegetables)
Total = 67 + 93 + 60 - (26 + 21 + 20) + 10
Total = 280 - 57
Total = 223
Therefore, the number of college students who do not like any of the three vegetables is 280 - 223 = 57.