The total number of ways in which 30 mangoes can be distributed among 5 persons is

Options

A. `""^(30)C_(5)`
B. `30^(5)`
C. `5^(30)`
D. `""^(34)C_(4)`

Explanation

To solve the problem of distributing 30 identical mangoes among 5 persons, we can use the "stars and bars" theorem from combinatorics. Here’s a step-by-step solution:

### Step 1: Identify the problem
We need to distribute 30 identical mangoes to 5 different persons. Since the mangoes are identical, the order in which they are distributed does not matter.

### Step 2: Apply the stars and bars theorem
The stars and bars theorem states that the number of ways to distribute \( n \) identical items into \( r \) distinct groups is given by the formula:

...