SPS SPS ASFM Statistics 2021 May — Question 3 7 marks

Exam BoardSPS
ModuleSPS ASFM Statistics (SPS ASFM Statistics)
Year2021
SessionMay
Marks7
TopicCombinations & Selection
TypeArrangements with adjacency constraints
DifficultyStandard +0.3 This is a standard combinatorics problem involving arrangements with restrictions. Part (a) uses the 'treat as a block' technique (routine), while part (b) requires the 'gaps method' (slightly less routine but still a textbook exercise). Both are well-established A-level techniques with straightforward execution, making this slightly easier than average.
Spec5.01a Permutations and combinations: evaluate probabilities

The members of a team stand in a random order in a straight line for a photograph. There are four men and six women.
  1. Find the probability that all the men are next to each other. [3]
  2. Find the probability that no two men are next to one another. [4]

The members of a team stand in a random order in a straight line for a photograph. There are four men and six women.

\begin{enumerate}[label=(\alph*)]
\item Find the probability that all the men are next to each other. [3]

\item Find the probability that no two men are next to one another. [4]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS ASFM Statistics 2021 Q3 [7]}}