Indicate how many 5-card hands there are of each of the following kinds. a) A se
ID: 3282016 • Letter: I
Question
Indicate how many 5-card hands there are of each of the following kinds. a) A sequence is a hand consisting of five consecutive cards of any suit. How many different sequence hands are possible? b) A matching suit is a hand consisting of cards that are all of the same suit in any order. How many different matching suit hands are possible? c) A straight flush is a hand that is both sequence and a matching suit. How many different strait flush hands are possible? d) A straight is a hand that is a sequence but not a matching suit. How many possible straights are there? e) A flush is a hand that is a matching suit but not a sequence. How many possible flushes are there? Indicate how many 5-card hands there are of each of the following kinds. a) A sequence is a hand consisting of five consecutive cards of any suit. How many different sequence hands are possible? b) A matching suit is a hand consisting of cards that are all of the same suit in any order. How many different matching suit hands are possible? c) A straight flush is a hand that is both sequence and a matching suit. How many different strait flush hands are possible? d) A straight is a hand that is a sequence but not a matching suit. How many possible straights are there? e) A flush is a hand that is a matching suit but not a sequence. How many possible flushes are there? a) A sequence is a hand consisting of five consecutive cards of any suit. How many different sequence hands are possible? b) A matching suit is a hand consisting of cards that are all of the same suit in any order. How many different matching suit hands are possible? c) A straight flush is a hand that is both sequence and a matching suit. How many different strait flush hands are possible? d) A straight is a hand that is a sequence but not a matching suit. How many possible straights are there? e) A flush is a hand that is a matching suit but not a sequence. How many possible flushes are there?Explanation / Answer
a) we can have following order of sets of consecutive cards : {2,3,4,5,6}, [3,4,5,6,7} .. .......upto {10,J,Q,K,Ace)
so, there are 10-2+1=9 ways of consecutive cards. but here each card can be choosen from any of the four suit .
Thus to choose {2,3,4,5,6} , there are 4*4*4*4*4 ways =45 ways.
similarly this goes with all sets and thus there are 9*45 ways in total for a sequence to occur.
b) To choose 5 cards from 13 cards of one suit , there are 13C5 ways in total.
so For all the four types of suits , these ways adds four times= 4* (13C5) ways to get matching suit
c) now to choose five consecutive cards from one suit , there are only 9 ways to do it as described in a) part.
so , for all four suits , there are 9*4=36 ways to get a straight flush.
d) We get the total no. of ways for a sequence to occur =9*45 ways in part a)
total no. of ways to get a sequence and a matching suit = 36 ways in part c)
if we subtract c) from a) we will get the total ways to get a sequence but not a matching suit
i.e a straight = 9*45-36
e) total no. of matching suits = 4*( 13C5) in part b)
Total no. of matching suit and sequence both =36 in part c)
if we subtract c) from b) we get total ways to get a flush =4*(13C5)-36