Part A: 1. Use an example to show or explain how Permutations with like/identical elements can sometimes be the same as a Combination. The use of factorial notation is required in your explanation Hint: the best examples use questions about the number of available pathways from one point to another. 2. Explain the difference between permutations and combinations. This question is only worth 2 marks. Make sure to keep it simple, and you should use either on example or the general formula for each in your explanation 3. Answer each question as stated. Show each line of work for full solutions. a) How many ways are there to form a lineup of 9 starting players out of 14 players? (1A) b) Solve: C(8,3) (1A) c) Convert to Factorial Form: 11C₂ (1A) 4. Problem Solving using combinations a) A dealership has 7 different types of car and 4 types of truck. If they sold 5 vehicles, in how many ways could it be 4 cars and 1 truck? b) At Open Window Bakery, they like to show off their featured baked goods in a display case. Today they are going to display 3 of 5 flavours of donut, 2 out of 4 types of croissant and 2 out of their 5 muffin flavours. In how many ways could these 7 items be displayed in a straight line? 1b) Choose 1 of the following binomial expansions to solve. Make sure you complete ONLY ONE (1) of them as you will lose marks if you do more than one. You need to show the initial step where the coefficients from Pascal's Triangle are used. i. (a - 2b)5 ii. (x - y)² iii. (m² + 1/m)4
