To help plan the number of meals to be prepared in a college cafeteria, a survey was conducte 133 students ate breakfast. 183 students ate lunch. 277 students ate dinner. 66 students ate breakfast and lunch. 113 students ate breakfast and dinner. 90 students ate lunch and dinner. 50 students ate all three meals. How many students ate (a) At least one meal in the cafeteria? 912 students (b) Exactly one meal in the cafeteria? students (c) Only dinner in the cafeteria? students (d) Exactly two meals in the cafeteria? 269 students

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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To help plan the number of meals to be prepared in a college cafeteria, a survey was conducte
133 students ate breakfast.
183students ate lunch.
277 students ate dinner.
66 students ate breakfast and lunch.
113 students ate breakfast and dinner.
90 students ate lunch and dinner.
50students ate all three meals.
How many students ate
(a) At least one meal in the cafeteria?
912
students
(b) Exactly one meal in the cafeteria?
students
ム
(c) Only dinner in the cafeteria?
students
d) Exactly two meals In the cafeteria?
269
students
Transcribed Image Text:To help plan the number of meals to be prepared in a college cafeteria, a survey was conducte 133 students ate breakfast. 183students ate lunch. 277 students ate dinner. 66 students ate breakfast and lunch. 113 students ate breakfast and dinner. 90 students ate lunch and dinner. 50students ate all three meals. How many students ate (a) At least one meal in the cafeteria? 912 students (b) Exactly one meal in the cafeteria? students ム (c) Only dinner in the cafeteria? students d) Exactly two meals In the cafeteria? 269 students
Expert Solution
Step 1

Let B be the number of students who have taken breakfast, L be the number of students who have taken lunch and D be the number of students who have taken dinner.

Then according to our problem,

n(B)= 133, n(L)= 183, n(D)= 277,

n(B and L)= 66, n(B and D)= 113,

n(L and D)= 90, n(B and L and D)= 50.

We draw the venn diagram to solve the problem.

 

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