Practice section 8 of 10

From the 6 letters of the word SALOON, find the

(i) number of possible arrangements if no two vowels are next to each other, [2]

(ii) number of possible arrangements if the two O’s are separated, [2]

(iii) number of 3-letter code words that can be formed. [2]

(a) How many different nine-digit numbers can be formed from five 0 s and four 1 s such that no three 0 s are together? [4]

(b) Six people sit at a round table with eight identical chairs. Find the number of seating arrangements if

(i) there are no restrictions, [2]

(ii) the seats are numbered. [1]

There are 9 people including John, Mary and Gary. They are to arrange themselves into a row of 4 people and a circle of 5 people. Find the number of ways they can arrange themselves if

(i) there are no restrictions. [2]

(ii) John and Mary are beside each other. [3]

(iii) John, Mary and Gary are part of the group that forms a circle, and John and Mary are separated from each other. [2]

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

(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]

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]

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

(iii) all 4 colours must be used. [2]

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]

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

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

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

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