Using the combination formula, the probability that Ronnie is dealt 1 club, 1 diamond, 1 heart, and 2 spades is 0.066 or 6.6%.
The combination formula:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items to choose.
In this case, n = 52 and r = 5. So the total number of ways to be dealt 5 cards is:
C(52, 5) = 52! / (5!(52-5)!) = 2,598,960
The number of ways to be dealt 1 club, 1 diamond, 1 heart, and 2 spades:
The number of clubs in a standard 52-card deck = 13
The number of diamonds in a standard 52-card deck = 13
The number of hearts in a standard 52-card deck = 13
The number of spades in a standard 52-card deck = 13
The number of ways to be dealt 1 club, 1 diamond, and 1 heart is: C(13, 1) * C(13, 1) * C(13, 1)
= 13 * 13 * 13
= 2,197
The number of ways to be dealt 2 spades is: C(13, 2) = 78
The implication is that the number of ways to be dealt 1 club, 1 diamond, 1 heart, and 2 spades is: 2,197 * 78 = 171,546
Thus, the probability that Ronnie is dealt 1 club, 1 diamond, 1 heart, and 2 spades is approximately 0.066 or 6.6% (171,546 / 2,598,960).