SPM 2022 Add Maths Paper 1, Question 10Permutation & Combination

Solved on video in English and Bahasa Melayu · Form 5, Permutation & Combination · 9:18 video

The question

(a)(i)

10 (a) A school bookstore is having a stock clearance promotion which involves 8 different pens and 10 different notebooks. Anvi will spend RM24 in the promotion. Table 1 shows the prices for a unit of each item: Pen RM2.00, Notebook RM4.00. Find the number of different ways Anvi can buy the items if (i) she wants to buy notebooks only.

(a)(ii)

10 (a)(ii) Find the number of different ways Anvi can buy the items (with RM24, 8 different pens at RM2.00 each and 10 different notebooks at RM4.00 each) if the number of notebooks is at most equal to the number of pens.

(b)(i)

10 (b) Diagram 6 shows an example of a five-character password formed by using letters and digits on a computer screen (example shown: E N 7 e 4). Find the number of different passwords if (i) the first three characters are A8a without repetition.

(b)(ii)

10 (b)(ii) Find the number of different five-character passwords if the first character must be a non-vowel capital letter and is followed by at least two prime numbers placed adjacently.

SPM 2022 Add Maths Paper 1, Question 10: the question as drawn in Eduly's video9:18

Part (a)(i)

Step 1

With RM24 spent on notebooks only at RM4.00 each, the number of notebooks = 24 ÷ 4 = 6.

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

Final answer

10C6 = 210

Where students lose marks

Watch out: choosing 6 notebooks from 10 is picking a group, so use 10C6 = 210, not 10P6 = 151200.

Part (a)(ii)

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

Final answer

18105

Where students lose marks

Watch out: list every valid (x, y) pair. Stopping at (4, 4) misses (8, 2) and (6, 3), and each one adds to the total.

Part (b)(i)

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

Final answer

59P2 = 3422

Where students lose marks

Watch out: there are 10 digits (0 to 9), so 59 characters remain. Using 9 digits gives 58 × 57 = 3306, wrong.

Part (b)(ii)

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

Final answer

1291584

Where students lose marks

Watch out: repeats are allowed, so every prime position has 4 choices. Using 4, then 3, then 2 gives a wrong total.

Watch every step of this question solved on video (9:18), with the reason behind each step and a box that checks your own answer.

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