Final answer:
The probability that Ronnie is dealt a poker hand with 0 diamonds, 2 clubs, 2 hearts, and 1 spade is calculated by the combinations of possible selections from each suit and is found to be 3/100.
Step-by-step explanation:
To calculate the probability that Ronnie is dealt a poker hand with 0 diamonds, 2 clubs, 2 hearts, and 1 spade, we first need to realize that there are 13 cards of each suit in a standard 52-card deck. Using combinations, we can determine the number of ways to select the cards from each suit and then multiply these together to get the total number of ways to get such a hand.
The number of ways to choose 0 diamonds is simply 1, since we aren't picking any diamonds. For 2 clubs, there are 13 choose 2 possibilities, which is calculated as:
C(13, 2) = 13! / (2! * (13 - 2)!) = 13! / (2! * 11!) = 78
Similarly, for 2 hearts, there are also 13 choose 2 possibilities:
C(13, 2) = 78
For 1 spade, there are 13 choose 1 possibilities:
C(13, 1) = 13
To get the total number of successful outcomes, we multiply these combinations together:
78 (for clubs) * 78 (for hearts) * 13 (for spades) = 78 * 78 * 13 = 78,858
Finally, to find the probability, we divide this number by the total number of ways to choose 5 cards from the deck, which is 52 choose 5:
C(52, 5) = 52! / (5! * (52 - 5)!) = 2,598,960
The probability is therefore:
78,858 / 2,598,960 = 3/100
Hence, the probability that Ronnie is dealt 0 diamonds, 2 clubs, 2 hearts, and 1 spade is 3/100.