From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

Explanation

To solve the problem of selecting students for the excursion party, we will break it down into two cases based on the condition provided about the three students.

### Step-by-step Solution:

1. **Understanding the Problem**: We have 25 students in total, and we need to choose 10 students for an excursion party. Among these students, there are 3 students who have a special condition: they will either all join the party or none of them will.

2. **Case 1 - All 3 Students Join**:
- If all 3 of these special students join the party, we need to choose 7 more students from the remaining 22 students (since 25 - 3 = 22).
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