Emily buys a bag of cookies that contains 7 chocolate chip cookies, 6 peanut butter cookies, 4 sugar cookies and 5 oatmeal cookies.

What is the probability that Emily reaches in the bag and randomly selects 2 chocolate chip cookies from the bag? Round your answer to four decimal places.

To solve this problem, we will use the concept of **combinations** to find the probability.

### Step 1: Total number of cookies
Emily's bag contains:
- 7 chocolate chip cookies
- 6 peanut butter cookies
- 4 sugar cookies
- 5 oatmeal cookies

So, the total number of cookies is:
\[
7 + 6 + 4 + 5 = 22 \text{ cookies}
\]

### Step 2: Number of ways to choose 2 chocolate chip cookies
To find the number of ways to select 2 chocolate chip cookies from 7, we use the combination formula:

\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]

Here, \(n = 7\) and \(r = 2\), so the number of ways to choose 2 chocolate chip cookies is:

\[
\binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21
\]

### Step 3: Number of ways to choose any 2 cookies from 22 cookies
Now, we find the total number of ways to select 2 cookies from the entire bag of 22 cookies:

\[
\binom{22}{2} = \frac{22 \times 21}{2 \times 1} = 231
\]

### Step 4: Probability of selecting 2 chocolate chip cookies
The probability of selecting 2 chocolate chip cookies is the ratio of the number of favorable outcomes to the total number of possible outcomes:

\[
P(\text{2 chocolate chip cookies}) = \frac{\binom{7}{2}}{\binom{22}{2}} = \frac{21}{231}
\]

### Step 5: Simplification
\[
P(\text{2 chocolate chip cookies}) = \frac{21}{231} \approx 0.0909
\]

Thus, the probability that Emily selects 2 chocolate chip cookies is approximately **0.0909** (rounded to four decimal places).

Do you need further explanation or details on any of these steps?

Here are 5 related questions to explore further:
1. What is the probability of selecting 1 chocolate chip cookie and 1 peanut butter cookie?
2. How many ways can Emily choose 1 cookie of each type from the bag?
3. What is the probability of selecting 2 cookies that are not chocolate chip cookies?
4. What is the probability of selecting 3 cookies, all of the same type?
5. If 3 cookies are selected randomly, what is the probability that exactly 1 is a sugar

Emily buys a bag of cookies that contains 7 chocolate chip cookies, 6 peanut butter cookies, 4 sugar cookies and 5 oatmeal cookies. What is the probability that Emily reaches in the bag and randomly selects 2 chocolate chip cookies from the bag? Round your answer to four decimal places.

Find out how to calculate the probability of selecting 2 chocolate chip cookies from a bag of 22 cookies, including combinations of different types of cookies. This example uses combinatorics and basic probability concepts, suitable for high school students in Grades 9-12.

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