Review practice · Section 2 of 3

(a) Find the number of ways of arranging the word PRELIMINARY if the first and last letter is a vowel.4 marks

(b) A group of 10 students comprising 3 males and 7 females attended their graduation dinner. Find the number of ways of seating them at a round table with 10 chairs of different colours and no two male students seated next to each other.3 marks

A developer has recently completed a condominium project in HCI Valley. There are 5 blocks of buildings A, B, C, D and E as shown. The developer has 4 colours available. Each block can only be painted using a single colour. Find the number of ways to paint all 5 blocks if

(i) there are no restrictions,1 mark

(ii) block A and block B cannot be painted with the same colour,2 marks

(iii) all 4 colours must be used.2 marks

An office has 8 staff consisting of 5 employees,1 translator,1 secretary and 1 manager.

(i) The group stands in a line.

(a) Find the number of different possible arrangements.1 mark

(b) Find the number of different possible arrangements if the secretary and the manager do not stand together.2 marks

(ii) The group sits in a circle where the seats are indistinguishable.

(a) Find the number of different possible arrangements.1 mark

(b) Find the number of different possible arrangements if the secretary sits beside the manager, and the translator sits opposite the manager.2 marks

(a) A teacher wants to set a class test for 25 students. Each student receives the same questions, but in a different order. Find the least number of questions she must set.

(b) Sally has 12 chocolate bars: white 4, milk 3, dark 4 and hazelnut 1. She intends to give one bar each to three of her best friends in school.

(i) Find the number of ways she can do it.

(ii) One particular friend has a nut allergy and should not be given the hazelnut bar. Find the number of ways Sally can now give her friends the chocolates.

(a) Find the number of ways the letters of POSITIVE can be arranged if

(i) all vowels must be next to each other,2 marks

(ii) the vowels are separated and the arrangement begins and ends with I.2 marks

(b) The Mathematics Department of M Institute consists of 11 teachers, including Mr Tan and Mr Lin. At a meeting, all 11 teachers sit at a round table with numbered seats. How many arrangements have Mr Tan and Mr Lin next to each other?3 marks

After the meeting they find a circular table for 6 and a long table with a row of 5 seats at a food court, as shown. Find the number of arrangements of all 11 teachers at these two tables such that Mr Tan is seated next to Mr Lin.4 marks

(a) Five couples are to be seated at a round table with numbered seats. Find the number of ways such that each wife must sit next to her husband.3 marks

(b) Mr Lin wants to repaint his four bedrooms. Each room can only be painted with one colour. From six different colours, find the number of ways the four rooms can be painted if

(i) there is no restriction on the colours used,1 mark

(ii) there is no repetition of colours used,1 mark

(iii) he chooses exactly two colours.3 marks