In a party, there are 12 people with white shirts and 7 people with red shirts;
4 people have black shoes and white shirts;
5 people have black shoes and red shirts;
the total number of people with white or red shirts or black shoes is 21.
How many people have black shoes?
W−white shirtsR−red shirtsB−black shoes∣W∣=12,∣R∣=7,∣W∩R∣=0,∣W∩B∣=4,∣R∩B∣=5,∣W∩R∩B∣=0,∣W∪R∪B∣=21Inclusion−exclusion principle:∣W∪R∪B∣=∣W∣+∣R∣+∣B∣−∣W∩R∣−∣W∩B∣−∣R∩B∣+∣W∩R∩B∣⇒⇒∣B∣=21−12−7+4+5=11W-white\,\,shirts\\R-red\,\,shirts\\B-black\,\,shoes\\\left| W \right|=12,\left| R \right|=7,\left| W\cap R \right|=0,\left| W\cap B \right|=4,\left| R\cap B \right|=5,\left| W\cap R\cap B \right|=0,\left| W\cup R\cup B \right|=21\\Inclusion-exclusion\,\,principle:\\\left| W\cup R\cup B \right|=\left| W \right|+\left| R \right|+\left| B \right|-\left| W\cap R \right|-\left| W\cap B \right|-\left| R\cap B \right|+\left| W\cap R\cap B \right|\Rightarrow \\\Rightarrow \left| B \right|=21-12-7+4+5=11W−whiteshirtsR−redshirtsB−blackshoes∣W∣=12,∣R∣=7,∣W∩R∣=0,∣W∩B∣=4,∣R∩B∣=5,∣W∩R∩B∣=0,∣W∪R∪B∣=21Inclusion−exclusionprinciple:∣W∪R∪B∣=∣W∣+∣R∣+∣B∣−∣W∩R∣−∣W∩B∣−∣R∩B∣+∣W∩R∩B∣⇒⇒∣B∣=21−12−7+4+5=11
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