SOLUTION: How many five card hands consisting of 2 kings and 3 aces can be dealt from a deck of 52 playing cards?

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Question 1157058: How many five card hands consisting of 2 kings and 3 aces can be dealt from a
deck of 52 playing cards?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
How many five card hands consisting of 2 kings and 3 aces can be dealt from a
deck of 52 playing cards?
4 suits CHOOSE 2 for the kings = 4C2 = (4×3)/(2×1) = 12/2 = 6 ways.  They are


K♥ K♦  .  .  .
K♥ K♠  .  .  . 
K♥ K♣  .  .  .
K♦ K♠  .  .  .
K♦ K♣  .  .  .
K♠ K♣  .  .  .

For every one of those 6 ways to have the kings, we can put 3 aces with them any
of:

4 suits CHOOSE 3 for the aces = 4C3 = (4×3×2)/(3×2×1) = 24/6 = 4 ways.  

They are:

.  .  A♥ A♦ A♠
.  .  A♥ A♦ A♣
.  .  A♥ A♠ A♣
.  .  A♦ A♠ A♣

That's 6 times 4 or 6×4 or 24 ways to have such a 5-card poker hand.
 
Edwin