Find the probability using combinations.A bag contains 6 cherry, 3 orange and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability that you have all cherry candies.

Number of ways to take any "three"

= C(11,3) = 165
number of ways to select 3 cherries from 6
= C(6,3) = 20
prob (3 cherries) = 20/165
= 4/33

direct way:
prob(3 cherries) = (6/11)(5/10)(4/9)
= 4/33

Well, the total number of candies in the bag is 6 + 3 + 2 = 11. So, when you reach in and grab 3 pieces, there are a total of 11C3 ways you can do that.

Now, since we want to find the probability of getting all cherry candies, there is only 1 way to do that, which is grabbing all 3 cherry candies.

So, the probability of grabbing all cherry candies is 1 out of 11C3. But hey, don't worry, that's not as complicated as it sounds! It simply means that there is only one favorable outcome out of all the possible outcomes.

Now, let me do some quick math for you. The value of 11C3 is actually (11!)/(3!(11-3)!), which simplifies to (11!)/(3!8!). And that equals 165.

Therefore, the probability of getting all cherry candies is 1/165. So, good luck grabbing those cherry candies! Just make sure you don't go bananas if things don't quite work out.

To find the probability of getting all cherry candies, we first need to find the total number of possible combinations of taking 3 candies from the bag.

The total number of candies in the bag is 6 (cherry) + 3 (orange) + 2 (lemon) = 11.

The number of ways to choose 3 candies from 11 is given by the combination formula:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of candies and r is the number of candies we want to choose.

In this case, n = 11 and r = 3. Plugging these values into the formula:

C(11, 3) = 11! / (3! * (11-3)!) = 11! / (3! * 8!) = (11 * 10 * 9) / (3 * 2 * 1) = 165

So there are 165 possible combinations of choosing 3 candies from the bag.

Now we need to find the number of combinations that have all cherry candies. Since there are 6 cherry candies in the bag, we need to choose all 3 from the 6 cherry candies.

C(6, 3) = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20

So there are 20 combinations that have all cherry candies.

Finally, to find the probability, we divide the number of combinations that have all cherry candies by the total number of possible combinations:

P(all cherry candies) = 20 / 165 = 4 / 33

Therefore, the probability of getting all cherry candies is 4/33.

To find the probability of getting all cherry candies, we need to find the number of ways to choose 3 cherry candies out of the total candies in the bag.

First, let's calculate the total possible outcomes, which is the number of ways you can choose any 3 candies out of the total number of candies in the bag.

Using combinations, we can calculate the total possible outcomes as:
Total possible outcomes = C(total candies, 3)

In this case, the total number of candies is 6 cherry + 3 orange + 2 lemon = 11 candies.

So, Total possible outcomes = C(11, 3)

Now, let's calculate the number of favorable outcomes, which is the number of ways you can select all 3 cherry candies.

Since we want to select all cherry candies, there is only 1 cherry candy left after each selection. So, the number of ways you can select all cherry candies is 1.

Therefore, favorable outcomes = 1

Finally, we can calculate the probability using the formula:
Probability = favorable outcomes / total possible outcomes

Probability = 1 / C(11, 3)

Let's calculate the probability using combinations:
Probability = 1 / [11! / (3! * (11-3)!)]
= 1 / [11! / (3! * 8!)]

Simplifying further:
Probability = 1 / [11 * 10 * 9 / (3 * 2 * 1 * 8 * 7 * 6)]
= 1 / [11 * 10 * 9 / 48]
= 1 * 48 / (11 * 10 * 9)
= 48 / 990

So, the probability of selecting all cherry candies is 48/990 or approximately 0.0485 (rounded to four decimal places).