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    The number of applications of the binomial coefficients is just as expansive as the number of identities we can find among the numbers.  This list is making no attempt to be thorough, but presents ideas that use the binomial coefficients that can be explained to people with modest mathematical experience.  If there are phrases or symbols unfamiliar to you in any of these presentations, we recommend looking in the FAQ, terminology and symbols page on this website.  If you still have unanswered questions, e-mail us, changing anything in (parentheses) in the address to make it legitimate.

What types of questions are answered by the binomial coefficients?
The Pascal's Triangle Card Trick
How many different poker hands are there?
What number greater than 1 shows up most often in Pascal's Triangle?
If you flip a coin ten times, what are the odds of getting five heads and five tails? (Java)
What does Pascal's Triangle look like mod n? (Java)
How does Pascal's Triangle approximate normal distribution (the Bell Curve)? (Java)
How does the null hypothesis (H0) work in statistics? (Java)
What is the Problem of Points? (Java)
How many gifts in total does my true love give to me during "The 12 Days of Christmas"? (link to rutgers.edu)
The Ant Problem
How does orthogonality work? (Java)
What are B-splines? 
Powers of 11 and powers of 9                        
What is the Kruskal-Katona Theorem?
What is Vandermonde's Convolution? (Java) generalizes to