| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | September |
| Marks | 6 |
| Topic | Combinations & Selection |
| Type | Selection from categorized items |
| Difficulty | Moderate -0.8 Both parts are standard combinatorics problems requiring straightforward application of counting principles. Part (a) uses the classic 'arrange items with restrictions' technique (place girls first, then boys in gaps), while part (b) is direct application of combinations C(n,r). These are routine A-level Further Maths questions with no novel insight required, making them easier than average overall. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
\begin{enumerate}[label=(\alph*)]
\item 5 girls and 3 boys are arranged at random in a straight line.
Find the probability that none of the boys is standing next to another boy.
[3 marks]
\item A cricket team consisting of six batsmen, four bowlers, and one wicket-keeper is to be selected from a group of 18 cricketers comprising nine batsmen, seven bowlers, and two wicket-keepers.
How many different teams can be selected?
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q1 [6]}}