In the poker game “Five Card Draw" a player first receives five cards drawn at random.

The player decides to discard some of their cards and then receives replacement cards. Assume a player is dealt a hand with one pair and three unrelated cards and decides to discard the three unrelated cards to obtain replacements. Calculate the following conditional probabilities for the resulting hand after the replacements aremade.

(a) Obtaining a four-of-a-kind.

(b) Obtaining a three-of-a-kind.

(c) Obtaining two pairs.

(d) Obtaining a straight or a flush.

(e) Ending with one pair.