Review practice · Section 1 of 3

In each of the following cases, find the number of ways of forming a group of 10 people from 15 couples if each group contains

(i) exactly 5 couples,1 mark

(ii) no couples,2 marks

(iii) exactly 2 couples.3 marks

A student working on a coding project studies 11-digit quaternary sequences. A quaternary sequence is a sequence formed using the digits 0, 1, 2 or 3. Examples are 12030201131, 01122211100, 12321232123 and 00000000000. Find the number of ways that 11-digit quaternary sequences can be formed with

(i) no restriction,1 mark

(ii) exactly four 0 s and four 2 s,3 marks

(iii) at least two consecutive digits that are the same.3 marks

Joshua tries to recall the 6-digit PIN number for his ATM card. Assume 000000 is even and valid. How many possible numbers can there be if he remembers that:

(i) the number starts and ends with the digit 5?1 mark

(ii) the number is odd and the digits do not repeat?2 marks

(iii) the digits do not repeat and there are exactly 3 odd digits?2 marks

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 marks

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

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

(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 marks

(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 marks

(ii) the seats are numbered.1 mark

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 marks

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

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