2 Counting Problems

2 Counting Problems - Math 100 Partitioning Problem Martin...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 100 Partitioning Problem Martin H. Weissman 1. A first problem In this problem, students will be asked to answer the following question: Suppose that n is a positive integer. Let S be a set with 3 n elements. How many ways are there to divide S into three teams of n ? In other words, how many sets { A,B,C } are there, such that A,B,C are all subsets of S with n elements, A B = , B C = , and C A = ? To get started, we observe that the following choice-sequences are equivalent: First, divide S into three teams of n elements. Then, label the three teams first, second, and third. First, choose a subset T 1 of S with n elements and call it the first team. Then, choose a subset T 2 of S- T 1 with n elements, and call it the second team. Call the remaining elements of S the third team. We leave it to the students (in pairs and triples) to solve the problem from here....
View Full Document

Ask a homework question - tutors are online