The problem asks for the probability of being dealt 5 cards of the same suit in a standard deck of 52 cards.

To solve this, let's first break it down:

• A deck has 52 cards, and there are 4 suits.
• The probability of getting 5 cards all from the same suit involves two components:
  1. Choosing the suit (which can be done in 4 ways, since there are 4 suits).
  2. Once a suit is chosen, you need to choose 5 cards from the 13 cards of that suit.

The number of ways to choose 5 cards from a specific suit is given by the combination formula: $\binom{13}{5} = \frac{13 \times 12 \times 11 \times 10 \times 9}{5 \times 4 \times 3 \times 2 \times 1}$

Now, the total number of ways to choose any 5 cards from the entire deck of 52 cards is: $\binom{52}{5} = \frac{52 \times 51 \times 50 \times 49 \times 48}{5 \times 4 \times 3 \times 2 \times 1}$

Thus, the probability is: $\frac{4 \times \binom{13}{5}}{\binom{52}{5}}$

Looking at the provided options, the one that matches this setup is:

$\frac{4 \times \binom{13}{5}}{\binom{52}{5}}$

This corresponds to the second option in the image.

Would you like further details or a breakdown of the combinatorics? Here are 5 related questions to deepen your understanding:

1. How is the combination formula derived?
2. What is the difference between permutations and combinations?
3. How would the probability change if we dealt 7 cards instead of 5?
4. Can you calculate the exact probability for this problem?
5. How would the approach differ if the deck contained jokers?

Tip: Always pay attention to whether the problem asks for combinations (unordered selections) or permutations (ordered selections).