Find the number of ways in which 13 identical apples can be distributed among 3 persons so that no two persons receive equal number of apples and each can receive any number of apples.

Explanation

To solve the problem of distributing 13 identical apples among 3 persons such that no two persons receive the same number of apples, we can follow these steps:

### Step 1: Understand the Problem
We need to distribute 13 identical apples among 3 persons (let's call them A, B, and C) with the condition that no two persons can receive the same number of apples.

### Step 2: Calculate Total Distributions Without Conditions
First, we can calculate the total number of ways to distribute 13 identical apples among 3 persons without any restrictions. The formula for distributing \( n \) identical items into \( r \) distinct groups is given by:

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