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In a group of 16 students, five had blue eyes and nine had black hair. Five had neither...

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student09871 | Student, Grade 8 | eNoter

Posted October 26, 2013 at 5:34 AM via web

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In a group of 16 students, five had blue eyes and nine had black hair. Five had neither blue eyes nor black hair, while three had both blue eyes and black hair.

Find the number of students with:

(i) Non-black hair

(ii) Non-blue eyes

(iii) Blue eyes but not black hair

(iv) Black hair but not blue eyes

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted October 26, 2013 at 6:12 AM (Answer #1)

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In a group of 16 students, five had blue eyes and nine had black hair. Five had neither blue eyes nor black hair, while three had both blue eyes and black hair.

Let E represent the set of students with blue eyes and H represent the set of students with black hair.

`n(E) = 5`

`n(H) = 9`

`n(EuuH) = 3`

`n(E'uuH') = 5`

The number of students with:

1. Non-black hair: 16 - 9 = 7

2. Non-blue eyes: 16 - 5 = 11

3. Blue eyes but not black hair: 5 - 3 = 2

4. Black hair but not blue eyes: 9 - 3 = 6

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