SPM 2024 Add Maths Paper 1, Question 11Permutation & Combination

Solved on video in English and Bahasa Melayu · Form 5, Permutation & Combination · 6:36 video

The question

(a)

(a) There are (n + 1) points on the circumference of a circle. If each point is connected by a straight line to all of the other points, there are 4n straight lines formed. Polygons can be formed by connecting points on the circumference of the circle. Find the total number of polygons that are possible.

(b)(i)

(b) A dormitory consists of 5 bunk beds. Each bunk bed has a top bed and a bottom bed. Table 1 shows the weights of 10 boys to be placed in the dormitory. Students A and B are twins. (Table 1: Student A B C D E F G H I J; Weight (kg) 49 52 45 40 66 48 61 56 48 47.) Find the number of different ways to arrange if (i) there is no restriction.

(b)(ii)

(b) Using the same dormitory setup and Table 1 as part (b)(i), find the number of different ways to arrange if (ii) students who weigh more than 50 kg are placed in a bottom bed and the twins are placed in the same bunk bed.

Part (a)

Step 1

The number of lines formed by choosing 2 points from (n + 1) is C(n+1, 2) = (n+1)n / 2.

Why this step

A line is just a pair of points, and AB is the same line as BA. Order doesn't matter, so use combination, not permutation.

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

Final answer

219 polygons

Where students lose marks

Watch out: a line joins two points and order doesn't matter, so use the combination C(n+1, 2), not permutation or circular arrangement formulas.

Part (b)(i)

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

Final answer

10! = 3 628 800 ways

Where students lose marks

Watch out: 5 bunks means 10 beds. Arrange all 10 boys with ¹⁰P₁₀ = 10!, not ¹⁰P₅ = 30 240.

Part (b)(ii)

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

Final answer

14 400 ways

Where students lose marks

Watch out: combine the stages by multiplying, 5 × 24 × 120. Adding them (5 + 24 + 120 = 149) is wrong.

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