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