from a standard deck of cards, 3 cards are selected. what is the probability that 2 are diamond and 1 are clubs?
i got (13C2)(13C1) = (78)(13) = 1014 but its not on my multiple choice answers
A) 1/2600 B 39/850 C 11/850 D 1/22100
I think it's C
Your answer is not even a probability. It is the number of ways to pick cards.
The cards can be
DDC: 13/52 * 12/51 * 13/50
DCD: 13/52 * 13/51 * 12/50
CDD: 13/52 * 13/51 * 12/50
= 3*(13*13*12)/(52*51*50) = 39/850
To find the probability, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
There are 52 cards in a standard deck, so the total number of possible outcomes will be calculated using the combination formula (nCr). In this case, we are selecting 3 cards from the deck, so the total number of possible outcomes is given by: 52C3.
Number of favorable outcomes:
We want to select 2 diamond cards and 1 club card. Let's calculate the number of ways we can select these cards.
Number of ways to select 2 diamond cards:
There are 13 diamond cards in the deck, so the number of ways to select 2 diamond cards will be calculated using 13C2.
Number of ways to select 1 club card:
There are 13 club cards in the deck, so the number of ways to select 1 club card will be calculated using 13C1.
Since we want both events to occur at the same time (2 diamond cards and 1 club card), we multiply the number of ways to select the diamond cards by the number of ways to select the club card.
Now, let's calculate the probability:
Total number of possible outcomes: 52C3
Number of favorable outcomes: (13C2) * (13C1)
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = [(13C2) * (13C1)] / 52C3
Now, let's calculate the probability:
Probability = [(13 choose 2) * (13 choose 1)] / (52 choose 3)
Probability = [78 * 13] / 22100
Probability = 1014 / 22100
The simplified fraction of the probability is 39/850.
Therefore, the correct answer is B) 39/850.