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which option is the answer to the question in the image?

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).

What is the probability of being dealt 5 cards of the same suit?

Learn how to calculate the probability of being dealt 5 cards of the same suit using combinatorics and probability. This problem explores key mathematical concepts and applies combination formulas to determine outcomes.

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