Question

. Consider 5-card hands from a standard 52-card deck of cards (and consider hands as sets, so that the same cards in different orders are the same hand). In your answers to following questions you may use binomial coefficients and/or factorials. (Recall that there are 4 Aces, 4 Kings, and 4 Queens in the deck of cards)

a) How many different 5-card hands are there?

b) How many hands are there with no Aces?

c) How many hands are there with at least one Ace?

d) How many hands are there with at least one Ace and at least one King?

e) How many hands are there with at least one Ace, at least one King, and at least one Queen?

Answer #1

Images contain the answer for given questions.

Suppose you choose 5 cards from a standard 52-card deck (with 13
hearts, 13 spades, 13 clubs and 13 diamonds). How many different
choices of cards are possible if a. you can choose any 5 cards from
the deck? b. all 5 cards must be hearts? c. you must choose four
kings and one queen? d. you must choose 3 kings and no queens? e.
you must choose at least 1 king and at least 2 aces?

If you are dealing from a standard deck of 52 cards a) how many
different 4-card hands could have at least one card from each suit?
b)how many different 5-card hands could have at least one spade? c)
how many different 5-card hands could have at least two face cards
(jacks, queens or kings)?

he following question involves a standard deck of 52 playing
cards. In such a deck of cards there are four suits of 13 cards
each. The four suits are: hearts, diamonds, clubs, and spades. The
26 cards included in hearts and diamonds are red. The 26 cards
included in clubs and spades are black. The 13 cards in each suit
are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This
means there are four...

The following question involves a standard deck of 52 playing
cards. In such a deck of cards there are four suits of 13 cards
each. The four suits are: hearts, diamonds, clubs, and spades. The
26 cards included in hearts and diamonds are red. The 26 cards
included in clubs and spades are black. The 13 cards in each suit
are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This
means there are four...

The following question involves a standard deck of 52 playing
cards. In such a deck of cards there are four suits of 13 cards
each. The four suits are: hearts, diamonds, clubs, and spades. The
26 cards included in hearts and diamonds are red. The 26 cards
included in clubs and spades are black. The 13 cards in each suit
are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This
means there are four...

Q19. Consider an ordinary 52-card North American playing deck (4
suits, 13 cards in each suit).
a) How many different 5−card poker hands can be drawn from the
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...

Consider a standard deck of 52 playing cards. Each part of 19
and 20 is worth 3 points, while 21 is worth 10 points.
19. (a) How many three-card hands are possible?
(b) How many three-card hands consisting only of face cards
(jack, queen, king) are possible?
20. (a) How many five-card hands consisting entirely of hearts
are possible?
(b) How many three-card hands consisting only of face cards
(jack, queen, king) are possible?

5 cards are randomly selected from a standard deck of playing
cards. How many hands contain exactly 1 queen, 1 king and 2
aces?

Suppose that we draw two cards from a standard deck of 52
playing cards, where ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen
and king each appear four times (once in each suit). Suppose that
it is equally likely that we draw any card remaining in the
deck.
Let X be the value of the first card, where we count aces as 1,
jacks as 11, queens as 12, and kings as 13. Let Y be...

A standard deck of cards contains 52 cards. One card is selected
from the deck. (a) Compute the probability of randomly selecting a
five or queen . (b) Compute the probability of randomly selecting
a five or queen or ace . (c) Compute the probability of randomly
selecting an ace or diamond .

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