Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Options

A. 1000
B. 2000
C. 3000
D. 4000

Explanation

To solve the problem of selecting 9 balls from 6 red balls, 5 white balls, and 5 blue balls with the condition that each selection consists of 3 balls of each color, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Selection Requirement**: We need to select 3 red balls, 3 white balls, and 3 blue balls.

2. **Calculate the Ways to Select Red Balls**:
- We have 6 red balls and need to choose 3.
- The number of ways to select 3 red balls from 6 is given by the combination formula \( \binom{n}{r} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.
- Thus, the number of ways to select 3 red balls is:
\[ \binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6!}{3!3!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20 \]

3. **Calculate the Ways to Select White Balls**:
- We have 5 white balls and need to choose 3.
- The number of ways to select 3 white balls from 5 is:
\[ \binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5!}{3!2!} = \frac{5 \times 4}{2 \times 1} = 10 \]

4. **Calculate the Ways to Select Blue Balls**:
- Similarly, we have 5 blue balls and need to choose 3.
- The number of ways to select 3 blue balls from 5 is:
\[ \binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5!}{3!2!} = \frac{5 \times 4}{2 \times 1} = 10 \]

5. **Combine the Results**:
- To find the total number of ways to select 9 balls (3 of each color), we multiply the number of ways to select red, white, and blue balls:
\[ \text{Total Ways} = \binom{6}{3} \times \binom{5}{3} \times \binom{5}{3} = 20 \times 10 \times 10 \]

6. **Calculate the Final Result**:
- Now, we compute the total:
\[ 20 \times 10 \times 10 = 2000 \]

### Final Answer:
The total number of ways to select 9 balls from 6 red balls, 5 white balls, and 5 blue balls, with each selection consisting of 3 balls of each color, is **2000**.