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

Solved on video in English · Form 5, Permutation & Combination · 6:13 video

The question

(a)(i)

(a) A group consisting of 3 adults and 5 teenagers are seated at a round table. Find the number of different ways they can be seated if (i) there are no restrictions.

(a)(ii)

Find the number of different ways they can be seated if (ii) three adults are not seated together.

(b)

(b) In an entrance assessment paper for a private school, there are six questions in Section A and seven questions in Section B. Candidates must answer 10 questions with the condition that at least four questions are from Section A and not more than five questions are from Section B. Find the number of ways a candidate can answer 10 questions in the examination.

Selangor Trial 2025 Add Maths Paper 1, Question 11: the question as drawn in Eduly's video6:13

Part (a)(i)

Step 1

There are 3 + 5 = 8 people seated around a round (circular) table.

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

Final answer

5040 ways

Where students lose marks

Watch out: a round table needs (n − 1)!, so use 7!, not 8!. Count all 8 people, adults and teenagers.

Part (a)(ii)

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

Final answer

4320 ways

Where students lose marks

Watch out: after finding 720 (adults together), subtract it from 5040. Use 5! for the block and don't forget the inner 3!.

Part (b)

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

Final answer

161 ways

Where students lose marks

Watch out: only (5, 5) and (6, 4) are valid, so A = 4 is out. Use combinations, and add the two cases, don't multiply.

Watch every step of this question solved on video (6:13), with the reason behind each step and a box that checks your own answer.

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