What is the sample space of being dealt exactly three 4's in a 5-card hand from a standard 52-card deck?

Answer 1

The sample space of being dealt exactly three 4's in a 5-card hand from a standard 52-card deck can be calculated by considering the following:

1. There are a total of 52 cards in a standard deck.
2. There are 4 cards that have the value of 4 in the deck.
3. We want to be dealt exactly three 4's in a 5-card hand.

Therefore, the sample space can be calculated using the combination formula:

\[ {4 \choose 3} \times {48 \choose 2} \]

\[ = 4 \times 1128 \]

\[ = 4512 \]

So, the sample space of being dealt exactly three 4's in a 5-card hand from a standard 52-card deck is 4512.