排列組合,probability問題 ,20點?

[匿名]

2016-03-29 2:18 am

A poker hand consists of seven cards drawn from a deck of 52 playing cards.

(a) How many different 7-card poker hands can be found?

(b) How many 7-card poker hands contain cards of the same suit?

(c) How many 7-card poker hands contain three cards of one kind and four cards of a second kind?

(d) What is the probability that a 7-card poker hand contains 7 consecutive cards? ( Note that an Ace can be considered either the lowest card of an A-2-3-4-5-6-7 or the highest card of an 8-9-10-J-Q-K-A). Give answer correct to 2 significant figures.

回答 (1)

Lopez

2016-03-29 6:06 am

✔ 最佳答案

(a)
C( 52 , 7 )
= 133784560 ... Ans

(b)
所求排列數
= 花色選擇數 * 該花色選7張
= 4 * C( 13 , 7 )
= 4 * 1716
= 6864 ... Ans

(c)
所求排列數
= ( 三條的牌號選擇數 * 三條的花色選擇數 ) * ( 四條的牌號選擇數 * 四條的花色選擇數 )
= [ 13 * C(4,3) ] * [ 12 * C(4,4) ]
= 13*4*12*1
= 624 ... Ans

(d)
數字最小者可能是 A , 2 , 3 , ..... , 8 , 故有 8 種可能的數字組合數

可能排列數
= 數字組合數 * 七張牌的花色組合數
= 8 * 4^7
= 8 * 16384
= 131072

所求機率
= 131072 / C( 52 , 7 )
= 131072 / 133784560
≒ 0.00098 ... Ans

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