SPM 2021 Add Maths Trial Paper (Selangor) – Paper 1 (Question 11 & 12)

Question 12:
(a) Find the number of ways to arrange each word SAKU and SAKA if no repetition is allowed. Are the number of arrangement that formed are the same?
Explain. [3 marks]

(b) Two boats are used to cross a river with each boat only able to carry 7 passengers. There are 9 adults and 4 children passengers.
If the number of children are the same on both boats, find the number of ways that these 13 passengers can be carried by the two boats. [2 marks]


Solution:
(a)

$\begin{array}{l}SAKU=4!=24\\ \\ SAKA=\frac{4!}{2!}=12\\ \\ \text{Not the same because SAKA has identical object }A\text{.}\end{array}$

(b)


$\begin{array}{l}\text{Maximum number of passengers in each boat = 7}\\ \\ \text{Number of ways to carry 13 passengers}\\ =\left({}^{9}C{}_5\times {}^{4}C{}_2\times {}^{4}C{}_4\times {}^{2}C{}_2\right)+\left({}^{9}C{}_4\times {}^{4}C{}_2\times {}^{5}C{}_5\times {}^{2}C{}_2\right)\\ =756+756\\ =1512\end{array}$