Learning Resources
Outcomes
In this lesson you will
- examine patterns in Pascal's Triangle
- relate the elements of Pascal's Triangle to combinations expressions
By the end of this section students will be able to:
- demonstrate an understanding of binomial expansion and its connection to combinations
- connect Pascal's triangle with combinatorial coefficients
Introduction
Mathematical Modeling, Book 3 p.340 - 345
Even though this section does not tie directly to probability it does tie nicely to the combinations and provides a useful "shortcut" to use when expanding binomials. It can be used to expand such expressions as 
without performing polynomial multiplication.
Binomial probabilities are based on binomial expansions. For example, in an experiment in which there are two outcomes with probabilities of 0.75 and 0.25, the probabilities of various outcomes after n trials is defined by the expression 
.
This section should take you about 2.5 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- patterns
- combinations