Please provide full solutions including proper notation for full marks. Show the formula used and how you substituted if required by the question. Hand it into the dropbox when finished. 1. In how many different ways can a photographer pose a row of 6 people without having the tallest person beside the shortest person? (2 marks) 2. In how many ways could a chairperson, treasurer, secretary and president be chosen from a 15-member board of directors? Show the ,P, value and the answer. (2 marks) 3. a) How many permutations are there of the letters in the word 'AVOCADO'? b) How many begin with the letter A ? c) How many start with C and end with the letter V ? (6 marks) 4. Rewrite each in the form , P, . (4 marks) a) 13 x 12 x 11 x 10 x 7 x 2 b) 111 x 112 x 114 x 113 5. Simplify each expression below. (4 marks) ( n+3 ) ! (n-1)! a) ( n+ 1 ) ! b) (n+7) x (n-2)