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A survey of $600$ schools in India was conducted to gather information about their online teaching learning processes $\text{(OTLP)}$. The following four facilities were studied.

$\text{F1}:$ Own software for $\text{OTLP}$

$\text{F2}:$ Trained teachers for $\text{OTLP}$

$\text{F3}:$ Training materials for $\text{OTLP}$

$\text{F4}:$ All students having Laptops

The following observations were summarized from the survey. 

  1. $80$ schools did not have any of the four facilities$ – \text{F1, F2, F3, F4}. $
  2. $40$ schools had all four facilities.
  3. The number of schools with only $\text{F1},$ only $\text{F2},$ only $\text{F3},$ and only $\text{F4}$ was $25,30,26$ and $20$ respectively.
  4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.
  5. $313$ schools had $\text{F2}.$
  6. $26$ schools had only $\text{F2}$ and $\text{F3} \; (\text{but neither F1 nor F4}).$
  7. Among the schools having $\text{F4}, 24$ had only $\text{F3},$ and $45$ had only $\text{F2}.$
  8. $162$ schools had both $\text{F1}$ and $\text{F2}.$
  9. The number of schools having $\text{F1}$ was the same as the number of schools having $\text{F4}.$

What was the total number of schools having exactly three of the four facilities$?$

  1. $200$
  2. $50$
  3. $80$
  4. $64$
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