turkey-yks 2018 Q26

turkey-yks · Other · yks-tyt Principle of Inclusion/Exclusion

For each of the 25 guests attending an opening, one glass each of mandarin juice, pomegranate juice, and orange juice was prepared and served to the guests. The following are known about these beverages served.

All guests took at least one type of beverage.
No guest took more than one glass of the same type of beverage.
No guest took exactly two types of beverages.

At the end of the opening, it was determined that 7 glasses of mandarin juice, 8 glasses of pomegranate juice, and 9 glasses of orange juice were not taken.
Accordingly, how many guests at this opening took all three types of beverages?
A) 7
B) 9
C) 11
D) 13
E) 15

For each of the 25 guests attending an opening, one glass each of mandarin juice, pomegranate juice, and orange juice was prepared and served to the guests. The following are known about these beverages served.

\begin{itemize}
  \item All guests took at least one type of beverage.
  \item No guest took more than one glass of the same type of beverage.
  \item No guest took exactly two types of beverages.
\end{itemize}

At the end of the opening, it was determined that 7 glasses of mandarin juice, 8 glasses of pomegranate juice, and 9 glasses of orange juice were not taken.

Accordingly, how many guests at this opening took all three types of beverages?

A) 7\\
B) 9\\
C) 11\\
D) 13\\
E) 15

Paper Questions

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