Question Detail
Question
In a sample of 1000 foodstuff sellers at a market, 200 stock rice, 240 stock beans, 250 stock flour, 64 stock both beans and rice, 97 stock both rice and flour, and 60 stock both beans and flour. If 430 stock none, how many stock all three?
Correct Answer
Option B is the correct answer.
Detailed Explanation
Number who stock at least one = 1000 − 430 = 570. Using inclusion-exclusion: 570 = 200 + 240 + 250 − 64 − 97 − 60 + x = 690 − 221 + x = 469 + x. So x = 570 − 469 = 101.
Hint
Start by finding those who stock at least one, then apply inclusion-exclusion.