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

Solved on video in English · Form 5, Permutation & Combination · 5:14 video

The question

(a)(i)

A robotics team consisting of 6 students will be selected from 4 boys and 3 girls.

(a)(i) Find the number of different teams that can be selected if there is no restriction.

(a)(ii)

(a)(ii) Find the number of different teams that can be selected if the team consists of at least 3 boys.

(b)

(b) Find the number of ways to choose and arrange all the boys and 2 girls for a photography session in a line, with the condition that all the boys must sit next to each other. (There are 4 boys and 3 girls in total.)

Melaka Trial 2025 Add Maths Paper 1, Question 11: the question as drawn in Eduly's video5:14

Part (a)(i)

Step 1

There are 7 students in total (4 boys + 3 girls) and 6 are chosen with no restriction; order does not matter, so use combinations.

Why this step

A team is just a group, so picking order does not matter. We use combinations, not permutations (⁷P₆), which is the common mistake here.

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

Final answer

7 teams

Where students lose marks

Watch out: a team is unordered, so use combinations ⁷C₆, not permutations ⁷P₆. Also count all 7 students.

Part (a)(ii)

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

Final answer

7 teams

Where students lose marks

Watch out: 'at least 3 boys' has two cases, exactly 3 and exactly 4. Count both and add them.

Part (b)

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

Final answer

432 ways

Where students lose marks

Watch out: choose 2 girls first (³C₂), and remember the boys can still arrange themselves inside their block (⁴P₄).

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