Given:
- 7 identical balls
- 5 different boxes

To find:
- Number of ways to distribute the balls

Approach:
- Use stars and bars method

Explanation:

- To solve this problem, we can use the stars and bars method.
- In this method, we use stars to represent the balls and bars to represent the boxes.
- We need to distribute 7 identical balls into 5 different boxes.
- Let's say we have 7 stars (representing the 7 balls) and 4 bars (representing the 5 boxes).
- We need to arrange these 7 stars and 4 bars in a line.
- The number of stars before the first bar represents the number of balls in the first box, the number of stars between the first and second bars represents the number of balls in the second box, and so on.
- The number of stars after the last bar represents the number of balls in the last box.
- For example, if we have the following arrangement of stars and bars:

**|***|**|****|*

- The first box contains 2 balls, the second box contains 3 balls, the third box contains 2 balls, the fourth box contains 4 balls, and the fifth box contains 1 ball.

- We need to find the number of ways to arrange 7 stars and 4 bars.
- This can be calculated using the formula:

(n + k - 1) choose (k - 1)

where n is the number of stars (balls) and k is the number of bars (boxes).

- Substituting the values, we get:

(7 + 5 - 1) choose (5 - 1)
= 11 choose 4
= 330

- Therefore, there are 330 ways to distribute 7 identical balls in 5 different boxes.

Answer:
- The correct answer is option B.