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