There are red, green and white identical balls each being 10 in number. The number of selections of 10 balls in which the number of red balls is double the number of green balls is ___________.

Answer

To solve the problem of selecting 10 balls such that the number of red balls is double the number of green balls, we can follow these steps:

### Step 1: Define Variables
Let:
- \( R \) = number of red balls
- \( G \) = number of green balls
- \( W \) = number of white balls

According to the problem, we have the following relationships:
1. \( R + G + W = 10 \) (total number of balls)
2. \( R = 2G \) (the number of red balls is double the number of green balls)

### Step 2: Substitute the Relationship
Using the second equation \( R = 2G \), we can substitute \( R \) in the first equation:
\[ 2G + G + W = 10 \]
This simplifies to:
\[ 3G + W = 10 \]

### Step 3: Express \( W \) in Terms of \( G \)
From the equation \( 3G + W = 10 \), we can express \( W \) as:
\[ W = 10 - 3G \]

### Step 4: Determine Possible Values for \( G \)
Since \( W \) must be a non-negative integer, we need to find the values of \( G \) such that \( 10 - 3G \geq 0 \):
\[ 10 \geq 3G \implies G \leq \frac{10}{3} \implies G \leq 3 \]
Thus, \( G \) can take the values \( 0, 1, 2, \) or \( 3 \).

### Step 5: Analyze Each Case
Now we analyze the possible values of \( G \):

1. **Case 1:** \( G = 1 \)
- \( R = 2G = 2 \)
- \( W = 10 - 3(1) = 7 \)
- Combination: \( (R, G, W) = (2, 1, 7) \)

2. **Case 2:** \( G = 2 \)
- \( R = 2G = 4 \)
- \( W = 10 - 3(2) = 4 \)
- Combination: \( (R, G, W) = (4, 2, 4) \)

3. **Case 3:** \( G = 3 \)
- \( R = 2G = 6 \)
- \( W = 10 - 3(3) = 1 \)
- Combination: \( (R, G, W) = (6, 3, 1) \)

### Step 6: Count the Valid Cases
We have three valid cases:
1. \( (2, 1, 7) \)
2. \( (4, 2, 4) \)
3. \( (6, 3, 1) \)

### Conclusion
The total number of selections of 10 balls in which the number of red balls is double the number of green balls is **3**.