Assignment:
Q1. How many subsets of {1, 1, 2, 2, 2, 3, 4, 4, 5} will contain a 2?
Q2. A group organizing Smith College's alumni reunion includes 6 current students, 8 current staff members and 11 alumni. Two individuals from each category will work on the publicity committee. Use combinations to determine the number of different publicity committees the group could form.
Q3. A gardener bought five geraniums, three rose bushes and four evergreen bushes from a nursery that had fourteen geraniums, twelve rose bushes and only five evergreen bushes. How many choices did the gardener have?
Q4. A 15-passenger shuttle bus takes athletes between vanues at the Canada Summer Games. If 32 athletes need to get to the track and field stadium, in how many ways can passengers be chosen for:
a) the bus's first trip?
b) the bus's second trip?
Provide complete and step by step solution for the question and show calculations and use formulas.