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 any number of candles.

Options

A. A) `2^12`
B. B) 240
C. C) 72
D. D) 12

Answer

To find the number of ways of selecting any number of candles from the given set, we can use the combinatorial principle of counting. Here’s a step-by-step solution:

### Step 1: Identify the number of each type of candle
- White candles: 2
- Red candles: 3
- Green candles: 4
- Yellow candles: 3

### Step 2: Understand the selection process
For each type of candle, we can select from 0 up to the maximum number available. This means:
- For white candles, we can select 0, 1, or 2 (which gives us 3 choices).
- For red candles, we can select 0, 1, 2, or 3 (which gives us 4 choices).
- For green candles, we can select 0, 1, 2, 3, or 4 (which gives us 5 choices).
- For yellow candles, we can select 0, 1, 2, or 3 (which gives us 4 choices).

### Step 3: Calculate the total number of selections
The total number of ways to select any number of candles can be calculated by multiplying the number of choices for each type of candle:
\[ \text{Total ways} = (\text{Choices for white}) \times (\text{Choices for red}) \times (\text{Choices for green}) \times (\text{Choices for yellow}) \]
Substituting the values:
\[ \text{Total ways} = (2 + 1) \times (3 + 1) \times (4 + 1) \times (3 + 1) \]
\[ = 3 \times 4 \times 5 \times 4 \]

### Step 4: Perform the multiplication
Now, we calculate:
\[ 3 \times 4 = 12 \]
\[ 12 \times 5 = 60 \]
\[ 60 \times 4 = 240 \]

### Final Answer
Thus, the total number of ways of selecting any number of candles is **240**.

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