(a) In the small country of Coland, car registration plates consist of different arrangements of groups of 4 letters taken from the Coland alphabet which consist of 10 letters. Calculate the number of different registration plates which can be made if (i) repetitions of letters are not allowed, (3 Marks) (ii) the letters can be repeated any number of times (2 Marks) In case (ii), all the different possible arrangements are listed and one arrangement is then to be chosen at random. Calculate the probability of choosing an arrangement which has (iii) two or more letters the same, (4 Marks) (iv) different letters at the beginning and the end of the arrangement. (4 Marks) (b) The student profile is to be selected as a prerequisite for the choice of a student representative. The student profile to be selected is based on the sex, represented by M for male or W for female, the year, from among first, second, third or fourth only and the whether or not the student is from a faculty F or from a college C. The format of a female student in second year belonging to a college may be represented by W2C. Suppose that all students are acceptable. If the student profile is selected randomly: (i) Give the sample space for the student profile. (2 Marks) (ii) Find the probability that the student profile selected is for a female faculty student. (2 Marks) (iii) Find the probability that the student profile selected is for a male student in a year below fourth year. (2 Marks) (iv) Find the probability that the student selected is female given that the student chosen is from a faculty