| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | May |
| Marks | 4 |
| Topic | Permutations & Arrangements |
| Type | Arrangements with grouped categories |
| Difficulty | Standard +0.3 Part (a) is a standard 'treat groups as single units' problem requiring 2!×6!×5! calculation. Part (b) requires placing men in gaps created by women (6!×P(7,5)), which is a common further maths permutations technique but slightly less routine. Overall slightly easier than average due to straightforward application of standard methods. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
13.
Six women and five men stand in a line for a photo.
\begin{enumerate}[label=(\alph*)]
\item In how many arrangements will all the men stand next to each other and all the women stand next to each other?
\item In how many arrangements will all the men be apart?
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q13 [4]}}