02 June 2008


P&C
Homework.
Show all necessary workings (You should not spend more than 1 hour on this part).

Orange bolded are the latest amendments .

(1) A computer game contains 12 different character classes, which are divided into three races as follow: 3 are Human, 4 are Elven and 5 are Dwarven. Players are asked to select 8 character classes. Calculate
(a) the number of different ways in which a player can select 8 characters if there is no restriction, Ans: 495
(b) the number of these selections which contain classes in only two of the character races, Human, Elven or Dwarven. Ans: 10

(2) 9 different books are to be arranged on a book shelf. 4 of these books were written by Shakespeare, 2 by Dickens and 3 by Conrad. How many possible permutations are there if
(a) there is no restriction on the arrangement of books, Ans: 362880
(b) the books by Conrad must be next to each other, Ans: 30240
(c) the books by Dickens are separated from each other. Ans: 282240

(3) Find the number of 5-letter code words that can be formed from the letters in the word INTEGRATED PROGRAMME, if the resulting code word cannot have any repeated letters.
Ans: 55440
(4) Calculate the number of arrangements of the letters of the word INCLUDE if
(a) all the consonants are together, Ans: 576
(b) each arrangement begins with a consonant and ends with a vowel. Ans: 1440

(5) The European Super League is a new football competition consisting of 8 teams. Fans are asked to submit predictions on the top 5 finishing teams in the correct order. The winner will be picked at random from those fans whose predictions are correct.
(a) Calculate the number of possible arrangements of 5 teams chosen from the 8, Ans: 6720
(b) If Bayern Munich is one of the 8 teams, calculate the number of these possible predictions
(i) in which Bayern Munich is placed first, Ans: 840
(ii) which contain Bayern Munich in one of the top 5 spots. Ans: 4200

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