A bag contains four 1-dollar bills, three 5-dollar bills, and two 10-dollar bills. You draw three bills but two of the bills has to be a five dollar bill.

Question

The event that at least two five dollar bills were drawn?

Answer 1

1 - (₆C₃ + 3*₆C₂)/₉C₃

_{This is the hypergeometric distribution for sampling WITHOUT replacement.}

_{The terms with C are binomial coefficients.}

_{The term subtracted is the probability of 0 or 1 5 dollar bill.}

_{If you wanted sampling WITH replacement, you would use the binomial.}