This assignment is out of 12 marks. To earn full marks for each question, a detailed algebraic solution andf'or explanation is required. Review the "Directing Words" chart found in the course introduction. {Zorn plete all questio ns before submitting this assignment for grading. Please contact your teacher if you have any questions. 1. Your math teacher is packing to vacation in a warm, sunny location and she does not want to pay the extra money for checked luggage. She needs to pack all her clothes in one small carry-on bag. She decides to take 4 different tops [a tank top, a t-shirt] and two different coloured blouses]. and 3 choices for bottoms (shorts. skirt and pants]. To accessorize she packs a scarf and a sweater. a. Draw a tree diagram to represent the number of different outfits she could make if she does not wear the scarf and sweater at the same time. {1 mark] h. Use the fundamental counting principle to determine the number of different outfrts for part a. [1 mark} c. Determine the total num ber of different outfits if your math teacher also includes the option of wearing the scarf and sweater at the same time. Hint: There are two cases to consider. [1 mark} 3. There are 1E} people lining up for a movie including three friends Annet Bradley:r and Carol. a. Determine the number of ways the line could be formed if the three friends will always stand together. [1 mark] la. Determine the number of ways the line oould he formed if the three friends stand together and Anne and Carol are always standing next to each other. {1 mark] 4. Prove that EC. = I,C'H, {Hint: algebraically shim-lI that the Left Side = Right Side] [1 mark]