Question

1.How many ways are there to draw a ﬁve-card poker hand that contains ﬁve cards of the same suit?

2. How many ways are there to draw a ﬁve-card poker hand that
contains at least one ace?

Answer #1

**Question 1:**

Number of suits = 4 ( spade, club, diamond, heart)

Number of cards in each suits = 13.

The possible cases to choose five cards.

**All five cards are spades or All five cards are diamonds
or all five cards are clubs or all five cards are
hearts.**

Hence total number of ways to choose five cards of the same suits is

**Answer - 5148**

**Question 2:**

Numbers of aces in a pack = 4

Number of remaining cards = 48

Possible cases are

**i) One ace and 4 remaining cards.**

**ii) two aces and 3 remaining cards.**

**iii) three aces and 2 remaining cards .**

**iv) 4 aces and 1 remaining card.**

Hence number of ways to choose 5 cards contains at least 1 ace is

=886656

**Answer - 886656.**

A standard 52-card poker deck consists of 4 suits and 13 ranks.
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2)all 5 cards are of same suits?
3) all four suits are present?
4) all cards are of distinct ranks?

In a 5-card poker hand, how many possible hands are there where
there are exactly 2 cards of the same value plus 3 other cards with
all different values none of which has the value 2. write down an
explanation for the answer.

Q19. Consider an ordinary 52-card North American playing deck (4
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deck?
b) How many different 13−card bridge hands can be drawn from the
deck?
c) What is the probability of an all-spade 5−card poker
hand?
d) What is the probability of a flush (5−cards from the same
suit)?
e) What is the probability that a 5−card poker hand contains
exactly 3 Kings...

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2. Assume that you play poker with six-card hands. (A straight
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low and there is no wrap-around. A flush has all six cards in the
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(f) How many six-card hands contain a straight?

5 cards are randomly selected from a standard deck of 52
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A card player is dealt a 13-card hand from a well-shuffled,
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I understand how we need to choose the cards but the only thing
that I do not understand is that how inclusion exclusion formula is
used in this question?
and how do I know that I need to use inclusion...

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