A hand offive-card poker consists of an unordered arrangement of five cards from an ordinary deck of 52 playing cards. Complete parts(a) through(e) below.

a. How many unorderedfive-card poker hands arepossible?

There are 25989602598960 differentfive-card draw poker hands. (Simplify youranswer.)

b. How many different hands consisting of one nine and four aces arepossible?

(Simplify youranswer.)

c. The hand in part(b) is an example of a fourofakind: four cards of one denomination and one of another. How many different fourofakinds arepossible?

(Simplify youranswer.)

d. Calculate the probability of being dealt a fourofakind.

(Round to five decimal places asneeded.)

e. Compare your answers in parts (a)-(d) to those for an ordered arrangement of five cards.

For an ordered arrangement of fivecards, there are 311,875,200 differentfive-card hands,

480 different hands consisting of one nine and four aces, 74,880 different fourofakinds,

and the probability of being dealt a fourofakind is about 0.00024.

Choose the correct answer below.

A.

There are fewer possible hands for unorderedhands, but there are also fewer possible

fourofakinds. The probability of a fourofakind is the same.

B.

There are more possible hands for unorderedhands, but there are also more possible

fourofakinds. The probability of a fourofakind

is the same

C.

There are more possible hands for unorderedhands, but there are fewer possible

fourofakinds. The probability of a fourofakind is smaller for unordered hands.

D.

There are fewer possible hands for unorderedh