The probability the a five card poker hand contains the ace of hearts, the king of diamond, and the queen of spades is: 9.62%
Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets.
Now,
A five-card poker hand selects 5 out of 52 cards. Therefore, by Permutations and Combinations:
C(52,5) = [tex]\frac{52!}{5! (52-5)!}[/tex] = 2598960
Now, we select the ace of hearts, for which we can withdraw any 4 out of 51 remaining cards. Therefore, by Permutations and Combinations:
C ( 51, 4) = [tex]\frac{51!}{4! (51-4)!}[/tex] = 249900
Finally, 249900 out of 2598960 hands contain a two of diamonds and a three of spades.
Thus, the probability = [tex]\frac{249900}{2598960} = \frac{5}{52}[/tex] (Approximately) ≈ 0.0962 = 9.62%
To learn more about Permutations and Combinations, refer to the link: https://brainly.com/question/11732255
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