# Binomial Coefficient and Factorial Notation

Not what you're looking for?

What is a binomial coefficient and factorial notation?

##### Purchase this Solution

##### Solution Summary

The binomial coefficent and the binomial distribution is explained. A simple example is used to illustrate.

##### Solution Preview

Ok, so first thing - binomial coefficient. You know that it is...

n choose k = n!/[(k!(n-k)!].

this is basically a way to count, right. It is counting that is unordered without replacement. This means that order doesn't matter. {1,2,3} is the same thing as {2,1,3}. Without replacement means that for each observation you make, the sample size shrinks by one. For example if you are choosing lottery numbers, each time a number is selected, that number can no longer be selected.

There are other types of counting, too, right. Ordered, w/ and w/out replacement, and unordered with replacement, as well.

Ok, so the binomial coefficient has to do with the binomial theorem, which maybe you have seen.

(x+y)^n = sum(0,n)[n choose k] (x^k) (y^n-k)

where n choose k is the binomial coefficient.

Lets do an example...

Expand

(x+y)^3 ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

##### Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.