Challenging +1.2 Part (a) is a standard 'treat groups as single units' problem requiring basic permutation counting. Part (b) requires more careful case analysis to handle the 'exactly 2 together, 1 separated' condition, involving selecting which 2 Calculus books are together and ensuring proper separation. While this demands systematic reasoning and careful counting, it remains a recognizable permutation problem type with moderate computational complexity, placing it somewhat above average difficulty.
8.
A teacher has 10 different mathematics books. Of these books, 5 are on Algebra, 3 are on Calculus and 2 are on Trigonometry.
The teacher arranges all 10 books in random order on a shelf.
a)
Find the probability that the Calculus books are next to each other and the Trigonometry books are next to each other.
\section*{In this question you must show detailed reasoning.}
b)
Find the probability that 2 of the Calculus books are next to each other but the third Calculus book is separated from the other 2 by at least 1 other book.
8.
A teacher has 10 different mathematics books. Of these books, 5 are on Algebra, 3 are on Calculus and 2 are on Trigonometry.
The teacher arranges all 10 books in random order on a shelf.\\
a)
Find the probability that the Calculus books are next to each other and the Trigonometry books are next to each other.
\section*{In this question you must show detailed reasoning.}
b)
Find the probability that 2 of the Calculus books are next to each other but the third Calculus book is separated from the other 2 by at least 1 other book.\\
\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q8 [7]}}