# Get a better hand

You are playing a game of poker, and you are dealt the following hand of cards from a shuffled standard poker deck:

$\text{A}\spadesuit, \text{A}\clubsuit, \text{A}\color{#D61F06}{\heartsuit}, 6\color{#D61F06}{\heartsuit}, 10{\color{#D61F06}{\diamondsuit}}.$

You put the $6\color{#D61F06}{\heartsuit}$ and $10\color{#D61F06}{\diamondsuit}$ cards aside, and request to be dealt two new cards.

What is the probability that you will improve your hand to a Four of a Kind or a Full House?

Note: Cards dealt to you are no longer in the deck. The $6\color{#D61F06}{\heartsuit}$ and $10\color{#D61F06}{\diamondsuit}$ cards are put aside; they are not put back into the deck.