Six straight lines are in a plane such that no two are parallel & no three are concurrent. The number of parts in which these lines divide the plane will be

Options

A. 15
B. 22
C. 29
D. 36

Answer

To find the number of parts in which six straight lines divide a plane, we can use the formula for the maximum number of regions (R) that n straight lines can create in a plane, given by:

\[ R(n) = \frac{n(n + 1)}{2} + 1 \]

### Step-by-Step Solution:

1. **Identify the number of lines (n):**
We have \( n = 6 \) straight lines.

2. **Substitute n into the formula:**
We will substitute \( n = 6 \) into the formula:
\[ R(6) = \frac{6(6 + 1)}{2} + 1 \]

3. **Calculate \( n + 1 \):**
First, calculate \( 6 + 1 \):
\[ 6 + 1 = 7 \]

4. **Multiply n by \( n + 1 \):**
Now, calculate \( 6 \times 7 \):
\[ 6 \times 7 = 42 \]

5. **Divide by 2:**
Next, divide \( 42 \) by \( 2 \):
\[ \frac{42}{2} = 21 \]

6. **Add 1 to the result:**
Finally, add \( 1 \) to \( 21 \):
\[ 21 + 1 = 22 \]

### Final Answer:
Thus, the number of parts in which six straight lines divide the plane is \( 22 \).