A survey of 500 farmers showed that of the​ farmers, 123 grew only​ wheat, 114 grew only​ corn, 94 grew only​ oats, 195 grew​ wheat, 61 grew wheat and​ corn, 47 grew wheat and​ oats, and 186 grew corn. Determine the number of farmers who ​a) grew at least one of the​ three, ​b) grew all​ three, ​c) did not grow any of the​ three, and ​d) grew exactly two of the three.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 36SE: The number of 5-element subsets from a set containing n elements is equal to the number of 6-element...
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A survey of

500

farmers showed that of the​ farmers,

123

grew only​ wheat,

114

grew only​ corn,

94

grew only​ oats,

195

grew​ wheat,

61

grew wheat and​ corn,

47

grew wheat and​ oats, and

186

grew corn. Determine the number of farmers who ​a) grew at least one of the​ three, ​b) grew all​ three, ​c) did not grow any of the​ three, and ​d) grew exactly two of the three.

 

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