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

Solved on video in English · Form 5, Permutation & Combination · 6:56 video

The question

(a)

In an intelligence quiz, symbols are arranged in Station A and Station B as shown in Diagram 3. Station A has 9 symbols (in a row) and Station B has 6 symbols (in a row). Find the number of triangles that can be drawn by using the symbols as vertices.

(b)

Diagram 3 shows the symbols in Station B (6 symbols, two of which are identical orange stars). Find the number of ways the symbols in Station B are arranged in a row.

(c)

Using the symbols in Diagram 3 (Station A: 9 distinct symbols; Station B: 6 symbols of which two are identical), find the number of ways if 3 symbols from Station A and 2 symbols from Station B are selected and arranged in a circle.

MRSM Trial 2025 Add Maths Paper 1, Question 11: the question as drawn in Eduly's video6:56

Part (a)

Step 1

A triangle needs 3 vertices that are not all collinear. All 9 symbols in Station A lie on one line and all 6 in Station B lie on another line, so 3 points chosen entirely from one station give no triangle.

Why this step

Three points on one straight line can't form a triangle. So we can't just use ¹⁵C₃ = 455, which wrongly counts flat triples.

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

Final answer

351

Where students lose marks

Watch out: ¹⁵C₃ = 455 wrongly counts three symbols on one line. Use both mixed cases: 2A + 1B and 1A + 2B.

Part (b)

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

Final answer

360

Where students lose marks

Watch out: 6! = 720 treats the two orange stars as different. Divide by 2! because they are identical.

Part (c)

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

Final answer

21168

Where students lose marks

Watch out: a circle uses (n − 1)!, not n!. The double-star case needs ÷ 2!. Don't miss any of the three cases.

Watch every step of this question solved on video (6:56), with the reason behind each step and a box that checks your own answer.

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