Holding unpaired cards and flopping EXACTLY trips by flopping two cards to one hole card.

You are looking any of the 6 cards that will pair one of your hold cards, then you are looking any of the 2 remaining cards that will trip that hole card, then you are looking for any card that DOES NOT quad up your hole card (that would give you 4 of a kind) and DOES NOT pair up your other hole card (that would give you a full house). Then divide by the number of combinations. That gives you:

(6 * 2 * 44 ) / (50 * 49 * 48) = 0.4489796%

That is the chance of flopping trips on the first two cards of the flop and a rag on the third. There are two other ways to flop trips that have an equal chance: (1) matching the first and third cards, (2) matching the second and third cards.

So, you have 3 * 0.4489796 = 1.347%.

Holding unpaired cards and flopping EXACTLY a full house, trips of one hole card and pairing the other.

You are looking any of the 6 cards that will pair one of your hold cards, then you are looking any of the 2 remaining cards that will trip that hole card, then you card looking for any of the 3 cards that will pair your other hole card. Then divide by the number of combinations. That gives you:

(6 * 2 * 3 ) / (50 * 49 * 48) = 0.03061224%

That is the chance of flopping trips on the first two cards of the flop and pairing on the third. There are two other ways to flop this type of full house that have an equal chance: (1) tripping the first and third cards while pairing the second, (2) tripping the second and third cards while pairing the first.

So, you have 3 * 0.03061224 = 0.0918%.

Holding unpaired cards and flopping EXACTLY four of a kind, three cards to one of your hole cards.

You are looking for any of the 6 cards that will pair one of your hold cards, then you are looking any of the 2 remaining cards that will trip that hole card, then you card looking for the 1 card that will quad that hole card. Then divide by the number of combinations. That gives you:

(6 * 2 * 1 ) / (50 * 49 * 48) = 0.0102%