Learning Goal: Solve complex counting problems involving the additive and multiplicative principles and other counting methods 3. Ms. Kelly organizing a board game day. There are 15 people who are coming (obviously this is pre-COVID). a) In how many ways can Ms. Kelly select 4 people to help her set up the room? b) There are too many people to all play one game, so Ms. Kelly will run 3 different groups. In how many ways can she select a group of 6, a group of 5 and a group of 4? c) Seven people are tired and a taking a break. They went for a walk. There are 8 people left to play games. If two games are being set up, and each game must have at least 2 players, in how many ways can these 8 people be grouped for the two games? d) The 15 people at the board game day party are divided into 6 adults and 9 children. Board games are being handed out at the end of the night as gifts. There are 10 adult board games, and 12 child board games to be handed out. In how many ways can these games be distributed? Learning Goal: Solve complex counting problems in a variety of ways Learning Goal: Use diagrams to solve counting problems 4. Choose one of the following questions to answer Level 4- Level 4+ A new supermarket was launched in A survey collects data from people about Kitchener. On opening day customers came what pets they like. The choices were cats, to the store and were asked how they dogs, and birds. The results were as follows: heard about the grand opening. They were -95 like cats informed via the following methods: 119 received flyers in the mail 165 like dogs - 131 learned about the launch through the - 93 like birds internet - 75 like cats and dogs - 140 heard about the launch through 20 like dogs and birds advertisements on television - 18 like cats and birds - 41 were aware of the launch through - 10 like none of those choices flyers and the internet - 35 came to know of it through flyers and There are 265 people surveyed television 16 heard about it from all three sources a) Construct a Venn diagram. b) Calculate n(D n C n B), what does that a) Construct a Venn diagram. mean in the context of this question? b) Calculate n(S), what does that mean in c) Calculate n(C'), what does that mean in the context of this question? the context of this question? c) Calculate n(F U T), what does that mean in the context of this