RI S1A Permutations and Combinations Add Prac Qns

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 6 _________________________________________________________________ Additional Practice Questions for Chapter S1A: Permutations and Combinations Page 1 of 6 Additional Practice Questions for Chapter S1A: Permutations and Combinations 1 From a group of 5 women and 7 men, one of whom is Mr Lee, find how many committees of size 4 can be formed in which (i) there are 2 men and 2 women, (ii) there is at least 1 man and at least 1 woman, (iii) there is at least 1 man and Mr Lee is in the committee. 2 4 boys, 4 girls and a teacher are to be seated at a round table. How many ways can they be arranged if (i) there is no restriction? (ii) the teacher is to be seated between any 2 girls? (iii) none of the boys are to be seated together? 3 How many 6-digit numbers (i) are even? (ii) begin and end with different digits? 4 A rectangular table has 7 secured seats, 4 being on one side facing the window and 3 being on the opposite side. In how many ways can 7 people be seated at the table (i) if 3 people, X and Y and Z must sit on the side facing the window? (ii) if 2 people, P and Q must sit on opposite sides? 5 A school is asked to send a delegation of six pupils selected from six badminton players, six tennis players and five squash players. No pupil plays more than one game. The delegation is to consist of at least one, and not more than three, players drawn from each sport. Giving full details of your working, find the number of ways in which the delegation can be selected. 6 Find the number of distinct arrangements of the letters of the word 'THERMOMETER' (i) if at least 2 'E's are together, (ii) which must start and end with 'T' or 'R'.

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ _________________________________________________________________ Additional Practice Questions for Chapter S1A: Permutations and Combinations Page 2 of 6 7 How many 4-digit numbers greater than 5000 can be formed from the digits 0, 1, 2, 3, 4, 5 if (i) no digit may be repeated? (ii) any digit may be repeated? (iii) only the digit 4 may be repeated? 8 A photographer is positioning 5 men and 4 women for a photo shoot. Find the number of ways the photographer can position them in a row (i) if no two people of the same sex are to stand next to each other, (ii) if the photographer positions the men in the order from shortest on the left to tallest on the right. (Assume that all the men are of different heights and are not necessarily standing together in a group.) 9 A box contains 9 balls. Out of these 9 balls, there are 3 identical red balls, 2 identical yellow balls and 4 numbered green balls (each labelled with a different number from 1 to 4). 3 balls are to be picked out of the box, and the order in which they are picked out does not matter. Find the number of possible selections of 3 balls. [3] 10 A painter is given a job to paint the doors of 5 adjacent rooms. Given that he has 5 colours of paint; red, blue, green, yellow and purple, find the number of ways he could accomplish his task if no adjacent doors are to be painted the same colour and (i) he must use two different colours only, (ii) he can use some or all of the colours. 11 The following diagram shows 12 distinct points on the sides of a triangle ABC. A (i) How many line segments are there joining any two points on different sides? (ii) How many triangles can be formed by joining any one point on side AB, any one point on side BC and any one point on B side AC? C

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ _________________________________________________________________ Additional Practice Questions for Chapter S1A: Permutations and Combinations Page 3 of 6 12 There are nine different waterslides at an amusement park. A person is allowed to go on each slide once only. However, he can choose to skip the slide or go on it. (i) If John goes on at least two slides at the amusement park, how many ways can he select the slides to go on? (ii) At another theme park, there are n different slides. John visits the theme park frequently and selects 2 slides to go on during every visit. At each visit, he makes a different selection, and first realizes that this was no longer possible on the 29th visit. Determine algebraically, the value of n. (iii) Give an example of a situation involving waterslides to which the expression ! !( )! n r n r is the solution. 13 A group of 10 people consists of 9 men and 1 woman. Find the number of ways which the group can be seated at a round table with identical chairs if (i) there is no restriction, [1] (ii) 2 particular men, Caleb and James, do not want to sit beside the woman, but will like to sit together. [3] The chairs at the table are replaced with 10 chairs of different colours. (iii) Find the number of ways which the group can be seated at a round table if Caleb and James must still sit together, but they need not be separated from the woman. [3] 14 2 men and 5 women go to a restaurant. They choose an outdoor round table with 7 seats for their meal. Find the number of ways the group can be seated if (i) the two men are not seated next to each other. [2] (ii) one of the women, Mary, is to be seated between the two men. [2] Before their orders arrive, they request to shift to a table in the 'non-smoking' section of the restaurant. They are then given a round table with 10 seats. Find the number of ways they can be seated if (iii) the empty seats are adjacent to each other. [2] (iv) none of the empty seats are adjacent to each other and there must be more than 1 person between any two empty seats. [2]

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ _________________________________________________________________ Additional Practice Questions for Chapter S1A: Permutations and Combinations Page 4 of 6 15 A soccer team consists of 3 goalkeepers, 8 defenders, 7 midfielders and 4 strikers. The coach has to select exactly 1 goalkeeper and 10 other players to start a match. (i) In how many ways can he select the 11 players? In each of the four sections (goalkeepers, defenders, midfielders and strikers), there is one STAR player. How many ways can the coach select his 11 players if (ii) he must include all the STAR players? (iii) he must include at least one STAR player? 16 Six identical boxes are arranged in 3 rows as shown in the following diagram. Sandra is given 1 green, 2 blue and 3 red balls. The balls are identical except for their colour. She is to put one ball in each box. Find the number of ways she can do this when (i) there is no restriction, [2] (ii) the balls in the bottom row are of different colours, [2] (iii) there are at least 2 red balls in the bottom row. [3] 17 Three couples who each have a child are to be seated at a round table with ten secured seats. Find the number of ways the nine people can be seated if (i) they do not mind who they are sitting with, [1] (ii) none of the children are to be seated on adjacent seats. [3] Mr Bean, who knows the three families well, is invited to take a seat at the table. Find the number of ways to seat the ten people if each child is to be seated adjacent to both his or her parents. [3] Top Row Middle Row Bottom Row

Raffles Institution H2 Mathematics 2025 Year 6 _______________________________