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)

SAKU=4!=24 SAKA= 4! 2! =12 Not the same because SAKA has identical object A.

(b)


Maximum number of passengers in each boat = 7 Number of ways to carry 13 passengers =( C 9 5 × C 4 2 × C 4 4 × C 2 2 )+( C 9 4 × C 4 2 × C 5 5 × C 2 2 ) =756+756 =1512

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