number of ways a random five-card hand can be formed so that the hand has exactly one pair?

Question

the deck is a standard 52 deck of cards.
the hand must have exactly one pair. the other three cards in the hand must be different.
a hand of three-of-a-kind does not qualify, a hand of two pairs does not qualify.

Answer 1

The number of ways a random five card pat hand can have exactly one pair is:

13*(4C2)*(48*44*40)/3!

= (13*6)*(48*44*40)/6 = 1,098,240

Answer 2

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