# Derivation of the probability distribution function of a binomial distribution

## Main Question or Discussion Point

Is there a way to derive

$$P (X=r) =^nC_r p^r q^{n-r} , r= 0, 1, 2,...., n$$

where $$X: B(n,p)$$

where n is the total number of bernoulli experiments,

p the probability of success

q, the probability of failure.