The coach of a football team selected 24 players for a tournament. He
picked 8 defenders, 7 midfielders, 5 strikers and 4 goalkeepers.

\begin{enumerate}
    \item \nbPointsEnumi{4}How many different teams can the coach put together if he chooses a
line-up consisting of 1 goalkeeper, 4 defenders, 3 midfielders and 3
strikers?

    \item \nbPointsEnumi{3}The coach has chosen 4 defenders in his line-up: Virgil, Sergio, Ruben
and Trent. The trainer can line up these defenders in the places
indicated by the blue dots. How many lineups are possible with these 4
defenders?
\end{enumerate}

\begin{center}
\includegraphics[width=2.01736in,height=2.83798in]{S6P3/2022_June/2022_06_S6P3_VAR_IT_BTest_ExoB1_IMG1.jpg}
\end{center}

\begin{enumerate}[resume]
    \item \nbPointsEnumi{3}For a press conference, a group of 4 players is randomly chosen from
all 24 players. Calculate the probability that this group consists of 1
defender, 1 midfielder, 1 striker and 1 goalkeeper.

    \item The probability that Christiano scores a penalty is 85\%. Christiano
kicks 5 penalties.

\begin{enumerate}
\item
  \nbPointsEnumii{2}Calculate the probability that Christiano scores 5 times.
\item
  \nbPointsEnumii{2}Calculate the probability that Christiano scores 3 out of 5
attempts.
\item
  \nbPointsEnumii{2}Calculate the probability that Christiano scores 4 times at
most.
\end{enumerate}
\end{enumerate}
