The question I am currently working with is as follows:
If three cards are randomly selected from a standard 52 card deck of playing cards, what is the probability that at least one of them will be a painted face card (king, queen or jack)?
Initially, I just went ahead and solved it as follows:
P(at least 1 will be a face card) = 1 - (40/52)*(39/51)*(38/50) = 55.29%
However, I went to solve it using the binomial distribution function just out of curiosity and got a slightly different answer:
P(at least 1 will be a face card) = 1 - (3 choose 3) * (40/52)^3 * (12/52)^0 = 54.48%