Learning Goal: Solve complex counting problems involving the additive and multiplicative principles and other counting methods 1. Ms. Kelly has blocks with the letters ABCDEFG on them. a) How many 7-letter words can she make? b) How many 4-letter words can she make? c) How many 3 or 4 letter words can she make? d) How many 7-letter words can she make that start with a vowel? e) How many 7-letter words can she make where AE and CD must be together? 2. There are 15 people in Ms. Kelly's Data management class. a) Ms. Kelly needs to pick 3 of them to make some measurements for a lesson. How many ways can she make this group? b) Ms. Kelly is making breakout rooms with 5-students in each group. She needs to make 3 groups. In how many ways can she make a set of 3 groups of 5 students with 15 students? No person may be in more than one group. c) The class has 7 people with black shirts, and 8 people with other colours. Ms. Kelly is making a single group of 5 students. At least 3 people in the group must have a black shirt. In how many ways can the group be made