How many 5-card hands with 2 clubs and 3 hearts can be dealt from a deck of 52 cards?
Select one:
O a. 22308
O b. 30822
O c. 82230
d. 32280
Answers
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a .). 22308. we is the correct answer
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Answer:
Explanation:
As there are less aces than kings in our
5
-card hand, let's focus on those. I will write the first ace as
A
and the second as
A
, the kings will be
K
.
Let's say that the first card is an ace.
In this case, there are
4
different hands possible:
A
A
KKK
,
A
K
A
KK
,
A
KK
A
K
and
A
KKK
A
Now let's imagine that the second card is an ace. We don't need to consider the first card since this is already covered by the first case.
Thus, we only have
3
different hands possible:
K
A
A
KK
,
K
A
K
A
K
and
K
A
KK
A
Now let the third card be an ace.
This time we have only
2
possible hands (the others we have already counted):
KK
A
A
K
and
KK
A
K
A
Last but not least, if the fourth card is an ace, we have just
1
possible hand:
KKK
A
A
Thus, in total, we have
4
+
3
+
2
+
1
=
10
possible
5
-card hands with
3
kings and
2
aces.