Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least two children?
There are 6 ways in which each child can choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least two children: 1. Two children choose each flavor: 6 x 3 = 18 2. Three children choose one flavor, and the other three choose another flavor: 3 x 3 = 9 3. Four children choose one flavor, and the other two choose another flavor: 3 x 2 = 6 4. Five children choose one flavor, and the other one chooses another flavor: 3 x 1 = 3 5. Six children choose one flavor: 3 x 1 = 3 6. Six children choose two flavors: 3 x 2 = 6 Total = 45 ways
