A random variable has a binomial distribution (with parameters n and p) if it is the number of "successes" in a fixed number n of independent random trials, all of which have the same probability p of resulting in "success." Under these assumptions, the probability of k successes (and n−k failures) is nCk pk(1−p)n−k, where nCk is the number of combinations of n objects taken k at a time: nCk = n!/(k!(n−k)!). The expected value of a random variable with the Binomial distribution is n×p, and the standard error of a random variable with the Binomial distribution is (n×p×(1 − p))^½. This page shows the probability histogram of the binomial distribution.