抽牌同花

“至少 4 张同花色”包含两种情况：恰好 4 张同花色或 5 张同花色。

总样本数：$\binom{52}{5}$。

• 恰好 4 张同花色：先选花色（4 种），再从该花色 13 张里选 4 张，最后第 5 张从其余 39 张里选 1 张：

$$4\binom{13}{4}\binom{39}{1}.$$

• 5 张同花色：选花色（4 种），再从该花色 13 张里选 5 张：

$$4\binom{13}{5}.$$

因此概率为

$$\frac{4\binom{13}{4}\binom{39}{1}+4\binom{13}{5}}{\binom{52}{5}}.$$

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英文解析

"At least 4 of the same suit" includes two situations: exactly 4 of the same suit or 5 of the same suit.

Total number of samples: $\binom{52}{5}$.

• Exactly 4 of the same suit: first choose the suit (4 types), then choose 4 of the 13 cards of the suit, and finally choose the fifth card from the remaining 39 cards:

$$4\binom{13}{4}\binom{39}{1}.$$

• 5 cards in the same suit: choose a suit (4 types), and then choose 5 cards from the 13 cards of this suit:

$$4\binom{13}{5}.$$

So the probability is

$$\frac{4\binom{13}{4}\binom{39}{1}+4\binom{13}{5}}{\binom{52}{5}}.$$