Question: Five cards are dealt from standard deck of 52 cards, what is the probability of being dealt 3 kings?
Here is what I have
P(3 kings)=
C(4,3) = 3 out of 4 kings being dealt
C(48,2 = 2 out of remaning cards to complete 5 card deal
C(52,5) = 5 cards dealt out of 52 card deck.
C(4,3) = 4
C(48,2) = 48!
2!(48-2)!= 48X47/2 = 24X47=1128
C(52,5) = 2598960
P(3KINGS) = 47 / 108290
Correct?
Yes, your calculations are correct.
To find the probability of being dealt 3 kings, you need to calculate the number of favorable outcomes (getting 3 kings) divided by the total number of possible outcomes (any 5-card combination from a standard deck of 52 cards).
The number of ways to get 3 out of the 4 kings is given by the combination formula: C(4,3) = 4. This means there are 4 ways to choose 3 kings out of the available 4 kings.
The number of ways to choose the remaining 2 cards from the remaining 48 non-king cards is given by C(48,2) = 1128. This means there are 1128 ways to choose 2 cards out of the available 48 non-king cards.
The total number of ways to choose any 5 cards from a standard deck of 52 cards is given by C(52,5) = 2598960.
Therefore, the probability of being dealt 3 kings is (4 * 1128) / 2598960 = 47 / 108290, which is approximately 0.00043479 or 0.04348%.
To calculate the probability of being dealt 3 kings out of 5 cards from a standard deck of 52 cards, you need to use the concept of combinations.
The total number of ways to choose 5 cards from a deck of 52 is given by C(52,5) = 2598960.
The number of ways to choose 3 kings out of the 4 available kings is given by C(4,3) = 4.
The number of ways to choose the remaining 2 cards (not kings) from the remaining 48 cards is given by C(48,2) = (48!)/(2!(48-2)!) = (48*47)/(2*1) = 1128.
Therefore, the probability of being dealt 3 kings is P(3 kings) = (Number of ways to choose 3 kings) * (Number of ways to choose 2 non-kings) / (Total number of ways to choose 5 cards):
P(3 kings) = (4 * 1128) / 2598960 = 4512 / 2598960 = 0.001737
So, the probability of being dealt 3 kings from a 5-card hand is approximately 0.001737, or 0.1737%.