QUESTION 5 [25 marks] a) The national debate association received application from 5 boarding school for hosting inter-school debate competition for year 2021 and 2022. How many ways may the association select the hosts for the competitions. i) If both can be held at the same school ii) If both cannot be held at the same school (2 marks) (2 marks) b) In how many ways can 12 people be divided into three groups having 5, 4 and 3 persons. (2 marks) c) A train carriage at the amusement park has 4 seats on each side. In how many ways can 6 girls and 2 twin boys sit if i) The boys sit opposite each other ii) The boys do not sit next to each other (3 marks) (3 marks) iii) These children later want to ride a merry go round, how many ways to sit them if the boys want to sit next to each other. (3 marks) d) In tennis championship, there are 45 matches, if each team plays one match with every other team, how many teams enter the championship? (4 marks) e) If there are six slots in a timetable, how many ways to arrange three different subject if: i) each subject has two periods (3 marks) ii) first subject three periods, second subject two periods and third subject one period. (3 marks)