three of a kind

2012-02-27 1:34 am
Find the number of combination of getting three of a kind.

Three of a kind, also called trips or a set, is a poker hand such as 2♦ 2♠ 2♣ K♠ 6♥ that contains three cards of the same rank, plus two cards which are not of this rank nor the same as each other.

http://en.wikipedia.org/wiki/List_of_poker_hands#Three_of_a_kind
更新1:

why 13C1 x 4C2 x 12C1 x 4C1 x 11C1 x 4C1 is wrong ?

回答 (2)

2012-02-27 2:35 am
✔ 最佳答案
http://en.wikipedia.org/wiki/Poker_probability

1 首先從13個號碼中選1個﹐然後對此號碼從四種花色中選三種

2 另外的兩張牌要從餘下的12個號碼選2個不同的號碼﹐每個號碼各有四種花色可以選取

因此組合數

= C(13,1)C(4,3)C(12,2)[C(4,1)]^2

= 54912
2012-02-27 2:11 am
13C1 x 4C2 x 12C1 x 4C1 x 11C1 x 4C1


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