H2MA Remedial _ Permutation Combination_Solution (RVHS)

Teacher’s copy 1 RVHS H2 Mathematics Remedial Programme Topic: Permutation & Combination Basic Mastery Questions 1. There are 5 boys and 7 girls. A team of 4 is to be formed by selecting from these 12 people. (a) Find the number of ways in which the team consists of either 4 boys or 4 girls. (b) Find the number of ways in which the team consists of exactly 2 boys and 2 girls. RVHS JC Skills Builder: Learn to reason that one of the parts of the question needs you to apply the Addition Principle, while the other requires the Multiplicative Principle. Click here or scan this to view video example on when to use Addition Principle! Click here or scan this to view video example on when to use Multiplicative Principle! Answer: (a) 40 (b) 210 (a) 57 44No. of ways C C 40= + = (b) 57 22No. of ways C C 210=  = 2. ACJC Prelim 9758/2021/Q7(i) A group of 12 students consists of 3 students from class A, 4 students from class B and 5 students from class C. Find the number of ways in which a committee of 8 students can be chosen from the 12 students if it includes at least 1 student from each class. [2] RVHS JC Skills Builder: First of all, l earn to observe that questions with phrases such as “at least”. “no t more than”, “at most”, etc, could be solved by Listing Out Cases OR using the Complementary approach. Then, click here or scan this to view video example on solving by Listing Out Cases! Then, click here or scan this to view video example on solving by Complementary approach!

Teacher’s copy 2 Answer: 485 12 9 8 8 8 8No. of ways C C C 495 9 1 485 = − − = − − = 3. YIJC Prelim 9758/2021/Q5(ii) 9 students consisting of 4 from Class A and 5 from Class B are seated at a round table with 10 chairs. How many different seating arrangements can be formed if no two students from Class A are seated next to each other? [2] RVHS JC Skills Builder: Such question that requires objects to be separated are best solve by “Slot-in” method. We do not usually use the Complementary approach. Click here or scan this to view video example on solving by “Slot-in” method! Click here or scan this to view video example on solving questions involving permutation of distinct objects in a circular arrangement! Answer: 43200 No of ways = 6 4(6 1)! 4! C−   = 43200 4. RI Prelim 9758/2021/Q8(i) This question is about arrangements of all eight letters in the word IMMUNITY. Show that the number of different arrangements of the eight letters that can be made is 10080.[1] RVHS JC Skills Builder: Click here or scan this to view video example on