Answer these questions based on the following information.
There are 2 white candles, 3 red candles, 4 green candles and 3 yellow candles in a brand new packet. All the candles are uniform in shape and size, except their colour, as told above.
Find the number of ways of selecting 1 white, 2 red, 3 green and 22 yellow candles.

Options

A. (A) 0
B. (B) 1
C. (C) 2
D. (D) 10

Answer

To solve the problem, we need to determine the number of ways to select the specified number of candles from the given quantities.

### Step-by-Step Solution:

1. **Identify the Requirements**:
- We need to select:
- 1 white candle
- 2 red candles
- 3 green candles
- 22 yellow candles

2. **Check Available Candles**:
- Available candles:
- 2 white candles
- 3 red candles
- 4 green candles
- 3 yellow candles

3. **Analyze Each Color**:
- **White Candles**: We need to select 1 from 2 available.
- The number of ways to choose 1 white candle from 2 is given by the combination formula \( C(n, r) \):
\[ C(2, 1) = \frac{2!}{1!(2-1)!} = 2 \]

- **Red Candles**: We need to select 2 from 3 available.
- The number of ways to choose 2 red candles from 3 is:
\[ C(3, 2) = \frac{3!}{2!(3-2)!} = 3 \]

- **Green Candles**: We need to select 3 from 4 available.
- The number of ways to choose 3 green candles from 4 is:
\[ C(4, 3) = \frac{4!}{3!(4-3)!} = 4 \]

- **Yellow Candles**: We need to select 22 yellow candles, but we only have 3 available.
- Since we cannot select 22 yellow candles from only 3 available, it is impossible to fulfill this requirement.

4. **Conclusion**:
- Since it is impossible to select 22 yellow candles from only 3 available, the total number of ways to select the required candles is **0**.

### Final Answer:
The number of ways to select 1 white, 2 red, 3 green, and 22 yellow candles is **0**.