Four boys picked 30 apples. The number of ways in which they can divide then if all the apples are identical is

Explanation

To solve the problem of how many ways four boys can divide 30 identical apples, we can use the "stars and bars" theorem from combinatorics. Here's a step-by-step solution:

### Step 1: Understand the Problem
We need to find the number of ways to distribute 30 identical apples among 4 boys. This can be represented as finding non-negative integer solutions to the equation:
\[ x_1 + x_2 + x_3 + x_4 = 30 \]
where \( x_i \) represents the number of apples received by the \( i^{th} \) boy.

### Step 2: Apply the Stars and Bars Theorem
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