SOLUTION: A survey of 830 workers in a plant indicated that 520 owned houses, 560 owned cars, 275 owned boats, 350 owned cars and houses, 220 owned houses and boats, 160 owned cars and boats

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Question 1145089: A survey of 830 workers in a plant indicated that 520 owned houses, 560 owned cars, 275 owned boats, 350 owned cars and houses, 220 owned houses and boats, 160 owned cars and boats, and 150 owned all three.
How many of the workers did not own any of the three items?
How many of the workers owned only two of the items?
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
(a)  First calculate the number of those workers who own at least one of the items.


     For it, calculate the alternate sum


         560 + 560 + 275 - 350 - 220 - 160 + 150 = 815.


     The rest 830 - 815 = 15 workers do not own any of the three items.    ANSWER



(b)  Only cars and houses   350 - 150 = 200.

     Only cars and boats    160 - 150 =  10.

     Only houses and boats  220 - 150 =  70.


     The subsets of workers counted in the previous 3 lines are DISJOINT.


     Therefore, the number of workers who own only two items is  220 + 10 + 70 = 300.    ANSWER

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For more details and explanations, read the lessons
    - Advanced problems on counting elements in sub-sets of a given finite set
    - Challenging problems on counting elements in subsets of a given finite set
in this site, where you will find many similar solved problems.


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