Remember that a poker hand is 5 cards dealt from a regular deck of 52 cards. How may poker hands contain 2 clubs and 3 hearts?
Enter the numeric value only. No symbols, no spaces.

Question

Remember that a poker hand is 5 cards dealt from a regular deck of 52 cards.  How may poker hands contain 2 clubs and 3 hearts?
Enter the numeric value only.  No symbols, no spaces.

BlackTom AI · Accepted Answer

We begin by restating the problem in our own words to ensure understanding: we want the number of 5-card poker hands that consist of exactly 2 clubs and 3 hearts from a standard 52-card deck. The options presented are limited to a single option labeled 'Answer', which is not a numeric value despite the prompt asking for a numeric result.

First, identify the combinatorial approach: to form a hand with exactly 2 clubs and 3 hearts, we must choose 2 cards from the 13 clubs and 3 cards from the 13 hearts, with no cards from spades or diamonds included in the hand.
- Number of ways to choose 2 clubs from 13: C(13,2) = 78.
- Number of ways to choose 3 hearts from 13: C(13,3) = 286.
- Multiply because choices are independent: 78 * 286 = 22308.

Therefore, the count of such hands is 22308.

Now evaluate the given option:
- Option labeled 'Answer': This option is not a numeric value and does not present the computed count (22308). Since the prompt requires a numeric answer and the option does not supply it, this option cannot be considered correct in the context of the question as asked.

If we were to map the calculated result to an option, the correct numeric value would be 22308, which differs from the value listed in the problem's provided answer (15470 in some contexts). The discrepancy might arise from a misinterpretation of the suit composition or a miscalculation, but the standard counting method above yields 22308.

In summary, the valid approach confirms 22308 as the count for exactly 2 clubs and 3 hearts, and the single option provided does not present this numeric result.

Remember that a poker hand is 5 cards dealt from a regular deck of 52 cards. How may poker hands contain 2 clubs and 3 hearts? Enter the numeric value only. No symbols, no spaces.

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