Lesson 14

\[\Pr[\text{“not all four suits”}]=1-\frac{\binom{4}{1}\binom{13}{3}\binom{13}{1}^3+\binom{4}{2}\binom{13}{2}^2\binom{13}{1}^2}{\binom{52}{6}}\ .\]

Indeed, if all four suits are present among the six cards, then either one of the suits appears three times, or two suits appear twice each. Here we used the rules of complement, sum, and product.