# Organized Counting/

How many subsets of {1, 1, 2, 2, 2, 3, 4, 4, 5} will contain a 2?

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.

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?

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?

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How many subsets of {1, 1, 2, 2, 2, 3, 4, 4, 5} will contain a 2?

We know that the number of subsets of set with n elements is 2n. Hence the number of subsets of the given set is equal to 29. If we consider the set {1, 1, 3, 4, 4, 5} (the set without 2), the number of subsets is 26. Hence the number of subsets that contain a 2 is given by the difference 29-26=7x26=448

A group organizing ...

#### Solution Summary

In this solution, organized counting is incorporated.