A person tries to form as many different parties as he can, out of his 20 friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?

Options

A. 1)92378
B. 2)92364
C. 3)92376
D. 4)92391

Explanation

To solve the problem step by step, we will break it down into two parts as indicated in the question.

### Step 1: Determine the size of each party for maximum combinations

1. **Understanding the Problem**: We have 20 friends, and we want to form parties with the same number of friends in each party. We need to find out how many friends should be invited at a time to maximize the number of different combinations of parties.

2. **Using Combinations**: The number of ways to choose \( r \) friends from \( n \) friends is given by the combination formula:
\[
...