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\begin{document}

\title{Episode 12\\ Combinatorics}
\subtitle{European section, season 01}
\date{}

\begin{frame}
  \titlepage
\end{frame}

%THE RULES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The rules}

{\large
\begin{center}
\begin{itemize}
\item 10 questions. 
\item 3 minutes per question.
\item At the end of the quizz, group papers are marked by the teacher.
\end{itemize}
\end{center}}
\end{frame}


%Question 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 1}% Multiplication

{\Large 
For every meal, a student has to choose between 6 starters, two main courses, two sides, 5 cheeses or yoghurt and 3 desserts. What is the number of possible meals ?
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 2} % Powers

{\Large 
A man wears only black and white. Every morning he picks randomly one pair of shoes (black or white), one pair of trousers (black or white), one shirt (black or white) and one overcoat (black or white). What is the number of possible outfits ?
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 3}% Arrangements

{\Large 
In horse racing terminology, a trifecta is a parimutuel bet in which the bettor must predict which horses will finish first, second, and third in exact order. If there are 12 horses in the race, how many different choices are there ?
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 4}% Powers

{\Large
Every morning, a man living in London picks randomly an umbrella before going out in the rain. He can choose between three different ones : one green, one red and one black. What is the number of possible choices for one week ?
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 5}% Multiplication

{\Large  
Mario Kart Wii is a famous racing game developed by Nintendo. In this game, the player must choose between 4 modes, 24 Nintendo characters, 8 vehicules for each character, 8 cups and 4 races per cup. What is the number of possible races ?
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 6} % Arrangements 

{\Large
A group of 120 people have to elect a board made of a Chairman, a vice-Chairman and a secretary. How many possible boards are there ? Anyone can be elected, but a different person must be elected for each post.
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 7}% Powers

{\Large 
Every week, a teacher picks randomly a pupil in a class of 36 to wipe away the board after each lesson. What is the number of possible choices for 5 weeks ?  
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 8}% Arrangements

{\Large 
Ten people have to be arrange in a line and handed out numbers from 1 to 10. What is the number of possible arrangements ? 
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 9}

{\Large 
How many distinct car licence plates are there consisting of seven characters, the first two and last two being letters and the middle ones digits ?
}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Question 10}% Powers

{\Large 
\begin{quote}As I was going to St Ives\\
I met a man with seven wives\\
Each wife had seven sacks\\
Each sack had seven cats\\
Each cat had seven kits\\
Kits, cats, sacks, wives\\
How many were going to St Ives? 
\end{quote}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
