Kuala Lumpur Trial 2025 Add Maths Paper 1, Question 11Permutation & Combination

Solved on video in English · Form 5, Permutation & Combination · 5:53 video

The question

(a)(i)

Diagram 6 shows 9 beads containing the letters C, A, M, P, F, I, R, E, S. (Solution using a listing method is not allowed.)

(a)(i) Find the number of different ways to arrange all the beads in a row.

(a)(ii)

)

(a)(ii) Aminah used a piece of string to connect all the beads to form a bracelet. How many different arrangements can be formed if the letters C, A and M are arranged so that they cannot be next to each other?

(b)

Kelvin bought a box of erasers that contains p different patterns of erasers. Given that the number of different ways for Kelvin to choose 3 erasers from the box is (91/3)(p − 2), find the value of p.

Kuala Lumpur Trial 2025 Add Maths Paper 1, Question 11: the question as drawn in Eduly's video

5:53

Part (a)(i)

Step 1

There are 9 distinct beads to arrange in a row.

Why this step

Check for repeated letters first: none here, so no dividing. We use all 9 beads, so it is the full 9!, not a smaller nPr.

1 more step, with the reason for it, in the full solution

Final answer

9! = 362880

Where students lose marks

Watch out: no letters repeat, so do not divide by anything. Use all 9 beads, so it is 9!, not nPr.

Part (a)(ii)

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

Final answer

7200

Where students lose marks

Watch out: a bracelet is a circle that can be flipped, so divide by 2. Use gaps for 'not next to each other'.

Part (b)

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

Final answer

p = 14

Where students lose marks

Watch out: 'choose' means combination, not permutation. Cancel (p − 2) from both sides, and reject the negative root p = −13.

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