An un contains & white balls and 10 green balls. If Vince chooses 7 balls at random from the urn, what is the probability that he will select 4 white bails and 3 green balls? Round your answer to 3 decimal places.

To find the probability that Vince will select 4 white balls and 3 green balls from an urn containing white balls and 10 green balls, we use the concept of combinations.

### Step 1: Define the problem
Let:
- \( w \) be the number of white balls in the urn.
- The total number of balls in the urn is \( w + 10 \).

Vince is selecting 7 balls at random, and we want to find the probability of selecting exactly 4 white balls and 3 green balls.

### Step 2: Calculate the number of favorable outcomes
The number of ways to select 4 white balls out of \( w \) white balls is given by:
\[
\text{Number of ways to select 4 white balls} = \binom{w}{4}
\]

The number of ways to select 3 green balls out of 10 green balls is given by:
\[
\text{Number of ways to select 3 green balls} = \binom{10}{3}
\]

### Step 3: Calculate the total number of possible outcomes
The total number of ways to select 7 balls from \( w + 10 \) balls is given by:
\[
\text{Total number of ways to select 7 balls} = \binom{w+10}{7}
\]

### Step 4: Calculate the probability
The probability \( P \) that Vince will select exactly 4 white balls and 3 green balls is given by:
\[
P = \frac{\binom{w}{4} \times \binom{10}{3}}{\binom{w+10}{7}}
\]

### Step 5: Substitute the values and simplify
Let's calculate the probability. Since the exact number of white balls \( w \) isn't given, I can outline the general form, or you can provide \( w \) to get a precise numerical answer.

Do you want to provide \( w \), or should I keep the answer in this general form?

Calculate the probability of selecting exactly 4 white balls and 3 green balls from an urn containing white balls and 10 green balls. Use combinations and probability theory to determine the likelihood of this event. Round your answer to 3 decimal places.

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