Suppose a poker hand contains seven cards rather than five. Compute the probabilities of the following poker hands: (a) a seven-card straight (b) four cards of one rank and three of a different rank (c) three cards of one rank and two cards of each of two different ranks (d) two cards of each of three different ranks, and a card of a fourth rank (e) three cards of one rank and four cards of each of four different ranks (f) seven cards each of different rank

a) 0.00031

b)  0.0017

c)  0.31

d) 0.00018

Step-by-step explanation:

attached below is the detailed solution

Total number of 7-poker cards are 52P7 = 133784560

A) Determine the probabilities of Seven-card straight

probability of seven-card straight = 0.00031

B) Determine the probability of four cards of one rank and three of a different rank

P( four cards of one rank and three of different rank ) = 0.0017

C) Determine probability of three cards of one rank and two cards of each two different ranks

P( three cards one rank and two cards of two different ranks ) = 0.31

D) Determine probability of two cards of each of three different ranks and a card of a fourth rank

P ( two cards of each of three different ranks and a card of fourth rank ) =  0.00018