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A big flower vase has 9 Lilys, 7 daisies, and 3 sunflowers. Two flowers are randomly selected without replacement. What is the probability of selecting two daisies? Express the answer in the simplest form of fraction.

To calculate the probability of selecting two daisies, we first need to find the total number of ways to choose 2 flowers out of the 19 flowers in the vase. This can be calculated using the combination formula:

nCr = n! / r!(n - r)!

where n is the total number of flowers (19 in this case), r is the number of flowers we want to choose (2 in this case), and ! denotes factorial.

So, the total number of ways to choose 2 flowers out of 19 is:

19C2 = 19! / 2!(19 - 2)! = 171

Next, we need to find the number of ways to choose 2 daisies out of the 7 daisies in the vase:

7C2 = 7! / 2!(7 - 2)! = 21

Finally, we calculate the probability of selecting 2 daisies by dividing the number of ways to choose 2 daisies by the total number of ways to choose 2 flowers:

Probability of selecting 2 daisies = 7C2 / 19C2 = 21 / 171 = 1/8

Therefore, the probability of selecting two daisies is 1/8.

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A standard deck of 52 cards contains four sults: hearts, diamonds, clubs, and spades. Each sult has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two heart cards. Express your answer in percent form rounding to the nearest hundredth.

To calculate the probability of drawing two heart cards, we first need to find the total number of ways of choosing 2 cards out of 52, and then determine the number of favorable outcomes (drawing 2 heart cards).

Total number of ways to choose 2 cards out of 52:
52C2 = 52! / 2!(52-2)! = 1326

Number of ways to choose 2 heart cards out of 13:
13C2 = 13! / 2!(13-2)! = 78

Now, we calculate the probability of drawing 2 heart cards:
Probability = Favorable outcomes / Total outcomes
Probability = 78 / 1326
Probability ≈ 0.0587

To express the answer in percent form, we multiply by 100:
Probability ≈ 5.87%

Therefore, the probability of drawing two heart cards is approximately 5.87%.