Subjects: Permutations and Combinations

Stereos, clothes shopping, blood types, batting orders, telephone numbers and postal codes are topics used to demonstrate the fundamental counting principle. Students are introduced to permutations in a very general way.

Saddling up horses for a trail ride introduces permutations with restrictions. Formulas and common-sense approaches are used to solve permutation problems, including circular and ring permutations.

Choices pervade our lives. From concrete examples to questions with restrictions, students count choices and solve problems involving combinations. Practical and technological examples are included.

This review of the basics of probability shows how permutations can be used to solve probability problems in which order plays a role. New technology in DNA fingerprinting is one of the applications featured.

The probability of card games demonstrates the application of combinatorics to probability problems. Explores questions involving complementary probabilities and the phrases “at least” and “at most.”

The connection between Pascal’s Triangle and binomial distribution is made using a model. Pascal’s Triangle is used to carry out binomial expansion and solve problems.

Expansions of powers of a binomial are examined from the point of view of patterns, including the link between the coefficients and Pascal’s Triangle. Binomial expressions are then expanded using the Binomial Theorem.

Combination locks and the Braille alphabet are some applications used to review the permutations and combinations module. Topics include the Fundamental Counting Principle, permutations, combinations, combinatorics and the Binomial Theorem.