There are three kinds of fruits in the market. How many ways are there to purchase 25 fruits from among them if each kind has at least 25 of its fruit available?

Answer

To solve the problem of how many ways there are to purchase 25 fruits from three kinds of fruits, we can use the combinatorial method known as "stars and bars." Here’s a step-by-step solution:

### Step 1: Define the Variables
Let:
- A = number of fruits of the first kind
- B = number of fruits of the second kind
- C = number of fruits of the third kind

We need to find the number of non-negative integer solutions to the equation:
\[ A + B + C = 25 \]

### Step 2: Apply the Stars and Bars Theorem
The stars and bars theorem states that the number of ways to distribute \( n \) identical items (in this case, fruits) into \( r \) distinct groups (the kinds of fruits) is given by:
\[ \binom{n + r - 1}{r - 1} \]

In our case:
- \( n = 25 \) (the total number of fruits)
- \( r = 3 \) (the three kinds of fruits)

### Step 3: Substitute into the Formula
Using the formula, we substitute \( n \) and \( r \):
\[ \binom{25 + 3 - 1}{3 - 1} = \binom{27}{2} \]

### Step 4: Calculate the Binomial Coefficient
Now we calculate \( \binom{27}{2} \):
\[ \binom{27}{2} = \frac{27!}{2!(27 - 2)!} = \frac{27!}{2! \cdot 25!} \]
This simplifies to:
\[ \binom{27}{2} = \frac{27 \times 26}{2 \times 1} = \frac{702}{2} = 351 \]

### Conclusion
Thus, the total number of ways to purchase 25 fruits from three kinds is:
\[ \boxed{351} \]