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Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

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To find the number of possible 5-card combinations with exactly one king from a 52-card deck, we firstly calculate the ways to select one king from the four available (4C1), then compute the ways to select the other 4 cards from the remaining non-king 48 cards (48C4). The total combinations is the product of these two multiplication 4 * 48C4.

To solve this, we need to select exactly one king from the 4 kings available in a deck and then select another 4 cards from the remaining 48 cards (since 52 - 4 (kings) equals 48). Using the combination formula, which is nCk = n! / [k!(n-k)!], we can calculate the combinations of these card selections.

Step 1: Determine the number of ways to select one king from four kings. It's equivalent to 4C1 = 4.

Step 2: Calculate the number of ways to select the rest 4 cards from the 48 non-king cards, which is 48C4.

Step 3: Multiply these results together to get the final number of combinations. So, the answer is 4 * 48C4.

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