SPM 2021 Add Maths Paper 1, Question 11Permutation & Combination

Solved on video in English and Bahasa Melayu · Form 5, Permutation & Combination · 6:32 video

The question

(a)(i)

Diagram 8 shows six numbered cards: 1, 2, 5, 6, 7, 9. Find the number of different ways to arrange all the cards in a row.

(a)(ii)

Using the cards 1, 2, 5, 6, 7, 9, four cards are to be arranged to form a proper fraction (a two-digit numerator over a two-digit denominator) such that the even-number cards are arranged side by side. Find the number of different proper fractions that can be formed.

(b)(i)

The combination of n objects from m different objects is given by mCn. State the minimum value of n.

(b)(ii)

Sarra bought a box of coloured pencils that contains p different coloured pencils. Given that the number of different ways for Sarra to choose 3 pencils from the box is 26(p − 2), find the value of p.

SPM 2021 Add Maths Paper 1, Question 11: the question as drawn in Eduly's video6:32

Part (a)(i)

Step 1

There are 6 distinct cards to arrange in a row.

Why this step

Cards sit in a row, so order matters. That makes this a permutation question, not a combination one.

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

Final answer

720

Part (a)(ii)

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

Final answer

72

Where students lose marks

Watch out: the even block can also straddle the fraction bar. Counting only numerator and denominator cases gives 48, not 72.

Part (b)(i)

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

Final answer

n = 0

Where students lose marks

Watch out: choosing none of the objects is a valid combination, so the minimum is n = 0, not n = 1.

Part (b)(ii)

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

Final answer

p = 13

Where students lose marks

Watch out: p!/(p − 3)! is p(p − 1)(p − 2), three factors. Writing p(p − 2) and cancelling wrongly gives p = 156.

Watch every step of this question solved on video (6:32), with the reason behind each step and a box that checks your own answer.

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