Question 1.

Three Mathematics books, five English books, four Science books and a dictionary are to be placed on a student’s shelf so that the books of each subject remain together.

(a)      In how many different ways can the books be arranged?                 

(4)

(b)      In how many of these will the dictionary be next to the mathematics books?

(3)

(Total 7 marks)

 

Question 2.

Six people are to sit at a circular table. Two of the people are not to sit immediately beside each other. Find the number of ways that the six people can be seated.

(Total 5 marks)

 

Question 3.

There are six boys and five girls in a school tennis club. A team of two boys and two girls will be selected to represent the school in a tennis competition.

(a)      In how many different ways can the team be selected?

(3)

(b)      Tim is the youngest boy in the club and Anna is the youngest girl. In how many different ways can the team be selected if it must include both of them?

(2)

(c)      What is the probability that the team includes both Tim and Anna?

(1)

(d)      Fred is the oldest boy in the club. Given that Fred is selected for the team, what is the probability that the team includes Tim or Anna, but not both?

(4)

(Total 10 marks)

Question 4.

A room has nine desks arranged in three rows of three desks. Three students sit in
the room. If the students randomly choose a desk find the probability that two out
of the front three desks are chosen.

(Total 5 marks)

Question 5.

 

Question 6.