QUESTION 1 (25 marks) (a) Given the word "INDEPENDENCE", (i) Determine the number of (A) distinct permutations, using all of the letters. (3 marks) (B) permutations that begin and end with the letter "E". (3 marks) (C) four letters can be formed, if each word does not begin with "IN" and repetition of the same letter is not allowed. (3 marks) (ii) Using all of the letters, calculate the probability that a permutation does not begins with letter "D" or "N". (7 marks) ( b ) A student will be taking a Probability test and the test is known to consist of 20 true- false questions. Calculate the number of different ways (1) the student can answer all of the questions. (2 marks) (ii) each question can be answered so that 7 are right. (3 marks) (iii) each question can be answered so that at least 17 are right. (4 marks)