TOTAL /20 Please provide full solutions (including proper notation) for full marks. Show the formula used and how you substituted, if required. Hand it into the assignment folder when finished. 1. In how many different ways can a teacher arrange a row of 7 students without having the tallest person beside the shortest? (2 marks) 2. In how many ways could a chairperson, treasurer, president and secretary be chosen from a 10-member board of directors? (2 marks) 3. If you know the answer to: HOW do you deal with REPEATING LETTERS in a permutation?, then answer the 3 questions below. If you do NOT know what to do, then GO BACK and view the video on the content page before proceeding. a) How many permutations are there of the letters in the word 'DISCRETE' ? b) How many begin with a S? c) How many end with a consonant? (6 marks) 4. Rewrite each in the form " . (2 marks) 8! a) 100 x 102 x 101 x 99 b) 6! 5. Simplify each expression below. (3 marks) (n-1)! (n+1)! a ) (n+7)x(n-2)! b) (n+3)! 6. Consider the word 'LEADING' : (4 marks) a) In how many different ways can the letters of this word be arranged in such a way that the vowels always come together? b) Use the complement to determine the number of arrangements of the letters where the vowels are NOT together