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.
Learn more about Card combinations