Moderate -0.3 This is a straightforward combinations question with standard counting principles. Part (a) uses basic combination formula and complementary counting for probability. Part (b) involves systematic case-by-case counting with digit constraints (first digit non-zero, all different). While multi-part and requiring careful organization, all techniques are standard textbook exercises with no novel insight required—slightly easier than average A-level.
8.
\begin{enumerate}[label=(\alph*)]
\item A group of four different letters is chosen from the alphabet of 26 letters, regardless of order.
\begin{enumerate}[label=(\roman*)]
\item How many different groups can be chosen?
\item Find the probability that a randomly chosen group includes the letter P .
\end{enumerate}\item A three-digit number greater than 100 is formed using three different digits from the ten digits $0,1,2,3,4,5,6,7,8,9$.
\begin{enumerate}[label=(\roman*)]
\item Show that 648 different numbers can be formed.
One of these 648 numbers is chosen at random.
\item Find the probability that all three digits in the number are even. (You are reminded that 0 is an even number.)
\item Find the probability that the number is even.\\[0pt]
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q8 [10]}}