The Nature of Mathematics, 12th Edition
Home
about dr. smith
glossary
transparencies
other books

Chapter1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
group projects
individual projects
links by topic
Section 12.2: Combinations

12.2 Outline

A.  Committee problem
      1. definition
      2. combination formula
      3. deck of cards
B. Pascal's triangle
      1. n choose r
      2. table entries
C. Counting with the binomial theorem
      1. binomial theorem
      2. number of subsets

12.2 Essential Ideas

Combinations
A combination of r elements selected from a set of n elements is an subset of r elements selected without repetitions. The order of selection is not important.

Counting Formulas

Combination formula: The number of ways of selecting r elements from a set with cardinality n in which the order of selection is not important is n!/r!(n - r)!.

Combinations by Pascal's Triangle
The number of ways of selecting r elements from a set with cardinality n in which the order of selection is not important is found by looking at the rth entry in the n row:

< Back to Section 2