SPM 2017 Add Maths Paper 1, Question 22Permutation & Combination
Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Permutation & Combination · 5:25 video
The question
Dahlia has a home decorations shop. One day, Dahlia received 14 sets of cups from a supplier. Each set contained 6 pieces of cups of different colours. (a) Dahlia chooses 3 sets of cups at random to be checked. Find the number of different ways that Dahlia uses to choose those sets of cups. (b) Dahlia takes a set of cups to display by arranging it in a row. Find the number of different ways the cups can be arranged such that the blue cup is not placed next to the red cup.
[4 marks]
5:25Step 1
Choosing 3 sets from 14 sets (order does not matter): number of ways = C(14,3) = 364.
Why this step
Picking a group of sets, the order you grab them doesn't matter, so we use a combination C(n, r), not a permutation.
3 more steps, each with the reason for it, in the full solution
Final answer
(a) 364, (b) 480
Where students lose marks
Watch out: when blue and red are glued together, they can still swap places, so use 5! × 2! = 240, not 5!.
Watch every step of this question solved on video (5:25), with the reason behind each step and a box that checks your own answer.
No card. Every past-year question on video, in English and BM.
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