Category Archives: Combinatorics

Q: What’s the chance of getting a run of K or more successes (heads) in a row in N Bernoulli trials (coin flips)? Why use approximations when the exact answer is known?

The original question was: Recently I’ve come across a task to calculate the probability that a run of at least K successes occurs in a series of N (K≤N) Bernoulli trials (weighted coin flips), i.e. “what’s the probability that in … Continue reading

Posted in -- By the Mathematician, -- By the Physicist, Combinatorics, Equations, Math, Probability | 45 Comments

Q: How do I count the number of ways of picking/choosing/taking k items from a list/group/set of n items when order does/doesn’t matter?

Mathematician: Suppose that we have a list containing three items, {A,B,C}, and we want to know how many different ways there are of choosing two items from this list. If we care about the order that items are selected from … Continue reading

Posted in -- By the Mathematician, Combinatorics, Math | 10 Comments