If you are dealt 7 cards from a shuffled deck of 52 cards, find the probability of getting four queens and three kings.
Answer
Final Answer: The probability of getting four queens and three kings when dealt 7 cards from a shuffled deck of 52 cards is \(\boxed{2.989881642545298 \times 10^{-8}}\).
Step 1 ：The total number of ways to draw 7 cards from a deck of 52 is given by the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial. In this case, n=52 and k=7, which gives us a total of 133784560 outcomes.
Step 2 ：The number of ways to draw 4 queens from 4 and 3 kings from 4 is given by the product of two combinations: \(C(4, 4)\) for the queens and \(C(4, 3)\) for the kings. This gives us 4 favorable outcomes.
Step 3 ：The probability of drawing 4 queens and 3 kings is then given by the ratio of the number of favorable outcomes (drawing 4 queens and 3 kings) to the total number of outcomes (drawing any 7 cards). This gives us a probability of 2.989881642545298e-08.
Step 4 ：Final Answer: The probability of getting four queens and three kings when dealt 7 cards from a shuffled deck of 52 cards is \(\boxed{2.989881642545298 \times 10^{-8}}\).
