Answer to Question #198867 in Discrete Mathematics for Vina

Question

Fourty (40) students go to a party wearing red, white and blue. Of these students, 17 wear red, 22 wear white, 25 wear blue. (Students do not necessarily wear only one colour.) Furthermore, 7 wear red and white, 12 wear blue and white, and 9 wear red and blue. Which one of the following alternatives is true? (Hint: first calculate the value of x, the unknown) 1. 5 students wear red only. 8 students wear white and blue, but not red. 3 students wear red and white, but not blue. 2. 2 students wear red only. 11 students wear white and blue, but not red. 6 students wear red and white, but not blue. 3. 2 students wear red only. 8 students wear white and blue, but not red. 3 students wear red and white, but not blue. 4. 5 students wear red only. 11 students wear white and blue, but not red. 6 students wear red and white, but not blue.

Answer 1

Let

$$N(R\cap B\cap W)=x$$

Then

$$1+x+9-x+x+7-x$$

$$+12-x+4+x+3+x=40$$

$$x=4$$

$1+x=5$

5 students wear red only.

$12 - 4=8$

8 students wear white and blue, but not red.

$7 - 4 = 3$

1. 5 students wear red only. 8 students wear white and blue, but not red. 3 students wear red and white, but not blue.