A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two folowers are randomly selected without replacement. What is the probability of selecting two carnations? Express the answer in simplest form of fraction.
There are 18 flowers in total, so the probability of selecting a carnation on the first draw is 6/18. Since we did not replace the selected flower, there are now only 17 flowers left, including only 5 carnations. Therefore, the probability of selecting a second carnation on the second draw is 5/17. To find the probability of both events happening (i.e. selecting two carnations in a row), we multiply the probabilities:
(6/18) * (5/17) = 30/306 = 5/51.
So the probability of selecting two carnations is 5/51.
Well, selecting two carnations out of the three types of flowers can be quite a puzzling task. Let's proceed with some clownish probability calculations!
To determine the probability, we need to find the number of ways we can choose 2 carnations out of the total number of flower combinations possible. Assuming that we randomly select two flowers from the vase without replacement, we can use the combination formula to calculate this.
The total number of flowers in the vase is 5 + 6 + 7 = 18.
Now, let's calculate the number of ways we can select 2 carnations from the 6 carnations.
We have 6 carnations, and we want to choose 2. This can be represented as 6C2.
6C2 = (6!)/(2!(6-2)!) = (6!)/(2!4!) = (6 x 5 x 4!)/(2!4!) = 15.
So, there are 15 possible ways to select 2 carnations from the vase.
Now, let's determine the total number of ways we can choose 2 flowers from the 18 in the vase.
Using the combination formula, we have 18C2 = (18!)/(2!(18-2)!) = (18!)/(2!16!) = 153.
Therefore, out of the 18 flowers, there are 153 total combinations of 2 flowers that can be selected.
So, the probability of selecting 2 carnations from the vase is 15/153.
However, if we simplify this fraction, we get 5/51.
Hence, the answer is 5/51. Good luck picking those carnations!
To find the probability of selecting two carnations, we need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of flowers in the vase is 5 begonias + 6 carnations + 7 tulips = 18.
To select two flowers without replacement, we will use the combination formula, which is given by:
nCr = n! / r!(n-r)!
Where n is the total number of flowers in the vase and r is the number of flowers we want to select (in this case, 2 carnations).
The number of ways to select 2 carnations from the 6 available is given by:
6C2 = 6! / 2!(6-2)!
= (6 x 5 x 4 x 3 x 2 x 1) / [(2 x 1)(4 x 3 x 2 x 1)]
= (720) / (2 x 24)
= 720 / 48
= 15
So, the number of ways to select two carnations is 15.
Now, let's find the total number of possible outcomes when selecting any two flowers from the vase:
18C2 = 18! / 2!(18-2)!
= (18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / [(2 x 1)(16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)]
= (18 x 17) / (2 x 1)
= 306 / 2
= 153
So, the total number of possible outcomes is 153.
Finally, we can calculate the probability of selecting two carnations by dividing the number of favorable outcomes (selecting two carnations) by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 15 / 153
Therefore, the probability of selecting two carnations is 15/153, which cannot be further simplified.
To solve this problem, we need to calculate the probability of selecting two carnations.
First, let's find the total number of ways we can select two flowers from a total of 18 flowers (5 begonias + 6 carnations + 7 tulips).
The number of ways to choose two flowers from 18 can be calculated using the combination formula: nCr = n! / (r! * (n-r)!), where n is the total number of flowers and r is the number of flowers we want to select.
In this case, we want to choose two flowers from 18, so the calculation is:
18C2 = 18! / (2! * (18-2)!)
Simplifying this expression:
18C2 = (18 * 17) / (2 * 1)
Now, let's find the number of ways to choose two carnations from the 6 available carnations.
We can use the combination formula again:
6C2 = 6! / (2! * (6-2)!)
Simplifying this expression:
6C2 = (6 * 5) / (2 * 1)
Now we can calculate the probability by dividing the number of ways to choose two carnations by the total number of ways to choose two flowers:
P(selecting two carnations) = 6C2 / 18C2
Substituting the values we calculated earlier:
P(selecting two carnations) = (6 * 5) / ((18 * 17) / (2 * 1))
Simplifying this expression:
P(selecting two carnations) = (30) / (153)
Therefore, the probability of selecting two carnations from the flower vase is 30/153, which is already expressed in simplest form as a fraction.