SPM 2020 Add Maths Paper 1, Question 23Permutation & Combination

Solved on video in English and Bahasa Melayu · 8 marks · Form 5, Permutation & Combination · 5:41 video

The question

(a)

Table 2 shows the number of girls needed to manage three stalls on a school carnival day: Food stall needs 4, Drink stall needs 2, Game stall needs 3. On that day, 9 students were assigned to manage the stalls. How many different ways can the students be assigned?

[4 marks]

(b)

The school wants to reward the students (in the three groups Food = 4, Drink = 2, Game = 3). A student is chosen at random as a leader among them to lead all the recipients. The chosen leader and her group members will lead the reception, followed by the other two groups. The students from the same group have to line up together. How many different ways can the students be arranged?

[4 marks]

SPM 2020 Add Maths Paper 1, Question 23: the question as drawn in Eduly's video5:41

Part (a)

Step 1

Choose 4 of the 9 students for the Food stall: C(9, 4) = 126.

Why this step

Only who ends up in a stall matters, not the order inside it, so we use combinations (C), not permutations (P).

3 more steps, each with the reason for it, in the full solution

Final answer

1260 ways

Where students lose marks

Watch out: the choices happen together, so multiply, not add, and shrink the pool each time (9, then 5, then 3).

Part (b)

6 more steps, each with the reason for it, in the full solution

Final answer

1728 ways

Where students lose marks

Watch out: list every case. The leader's group can be any of the 3, and the two blocks behind can swap (2!).

Watch every step of this question solved on video (5:41), with the reason behind each step and a box that checks your own answer.

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