Final answer:
To find the probability of getting 4 Aces and a King when drawing 5 cards from a standard deck, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. The probability is approximately 0.00000154.
Step-by-step explanation:
To find the probability of getting 4 Aces and a King when drawing 5 cards from a standard deck, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
There are 4 Aces and 4 Kings in a deck of 52 cards. To get 4 Aces and 1 King, we need to choose 4 Aces and 1 King from the deck. The number of ways to choose 4 Aces from 4 Aces is 1, and the number of ways to choose 1 King from 4 Kings is 4. Therefore, the number of favorable outcomes is 1 * 4 = 4.
The total number of possible outcomes is the number of ways to choose 5 cards from 52 cards, which is calculated using combination formula as C(52, 5) = 52! / (5! * (52 - 5)!), where n! is the factorial of n.
Substituting the values into the formula, we get C(52, 5) = (52*51*50*49*48) / (5*4*3*2*1) = 2,598,960.
Therefore, the probability of getting 4 Aces and a King when drawing 5 cards at the same time is 4 / 2,598,960 ≈ 0.00000154 (rounded to 8 decimal places).