counting techniques

1. Evaluate the following K[ /4 marks] a. 6! C. 8P8 b. 5P4 d. 2. In how many ways could Toyosi rearrange eight different plants? K[ /2 marks] 3. Mrs. Larraine will select three students to speak in front of the class. If she has thirty students, how many different ways can she select the order of the two students? K[ /2 marks] 4. How many different possible sum outcomes are there if four six-sided dies are rolled? K[ /2 marks] 5. Itohan's ice cream store has three different types of cones, three flavours, and two topping choices. If each customer can only select one cone, one flavour, and one topping, how many different ice cream combinations are possible? Answer this question using two different methods. I[/6 marks] 6. Denis can either make a password with seven capital letters or a password with four characters that could involve lowercase and capital letters. Which scenario would have more possible outcomes? By how much? I[/6 marks] 7. Explain the relationship between the fundamental counting principle and the permutation formula. Provide an example with your explanation. C[ /4 marks]