Three cards of the same suit

Text

From a deck of $40$ Neapolitan cards ($4$ suits of $10$ cards) we draw $3$ cards. What is the probability that they are all three of the same suit?

Solution

We use classical probability with combinations (the order of drawing is irrelevant).

• Possible cases: $\binom{40}{3} = \dfrac{40\cdot 39\cdot 38}{6} = 9880$.
• Favorable cases: first choose the suit ($4$ ways), then $3$ of the $10$ cards of that suit: $4\cdot\binom{10}{3} = 4\cdot 120 = 480$.

Hence $P = \frac{480}{9880} = \frac{12}{247} \approx \boxed{0.0486}.$