Answer these questions based on the following information.
Last Diwali Chhota Bheem got 10 distinct coloured candles placed in a row. Then he asked his friend to lit 3 candles.
Find the number of ways of selection of candles so that all the 3 candles are consecutive.

Options

A. 19
B. 20
C. 8
D. 66

Answer

To solve the problem of selecting 3 consecutive candles from a row of 10 distinct colored candles, we can follow these steps:

### Step 1: Understand the Problem
We need to find the number of ways to select 3 consecutive candles from a total of 10 candles arranged in a row.

### Step 2: Define the Variables
Let:
- \( n \) = total number of candles = 10
- \( k \) = number of consecutive candles to be selected = 3

### Step 3: Use the Formula
The formula to find the number of ways to select \( k \) consecutive items from \( n \) items is given by:
\[ \text{Number of ways} = n - k + 1 \]

### Step 4: Substitute the Values
Now we substitute the values of \( n \) and \( k \) into the formula:
\[ \text{Number of ways} = 10 - 3 + 1 \]

### Step 5: Calculate the Result
Now, we perform the calculations:
\[ 10 - 3 = 7 \]
\[ 7 + 1 = 8 \]
Thus, the number of ways to select 3 consecutive candles is 8.

### Final Answer
The number of ways to select 3 consecutive candles from 10 distinct candles is **8**.

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