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In a survey of $100$ students, it was found that $50$ used the college library, $40$ had their own library and $30$ borrowed books of these, $20$ used both the college library and their own, $15$ used their own library and borrowed books and $10$ used the college library and borrowed books. How many students used all the three sources of books ?

  1. $30$
  2. $28$
  3. $20$
  4. $25$
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we know that $P(A\cup B\cup C)=P(A)+P(B)+P(C)-P(A\cap B)-P(B\cap C)-P(C\cap A)+P(A\cap B\cap C)$

So $\implies 100=50+40+30-30-15-10+P(A\cap B\cap C)$

$\implies P(A\cap B\cap C)=100-75=25$

Option (D) is correct.

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