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The problem in the image states:

"7 people visited a marriage function in 3 different vehicles, each accommodating a maximum of 5 persons. In how many ways can they visit, such that they use all the 3 vehicles?"

### Solution:

1. **Understanding the distribution problem:**
   - We need to distribute 7 people into 3 vehicles.
   - Each vehicle must carry at least 1 person, and no vehicle can carry more than 5 people.

2. **Step 1: Breaking down the number of people into vehicles.**
   Since there are 7 people and all vehicles must be used, we need to find how to split 7 people into groups where each group has at least 1 person.

   This is a classic combinatorics problem of distributing people into groups with restrictions. The combination of groups is solved using the stars and bars approach and factorial calculation for permutations.

3. **Step 2: Distribution options**
   The only valid group distributions are:
   - (3, 2, 2): One vehicle has 3 people, and the other two vehicles have 2 people each.

4. **Step 3: Calculating the number of ways to assign people:**
   - First, choose 3 people to go in the vehicle carrying 3 people. This can be done in \( \binom{7}{3} = \frac{7!}{3!(7-3)!} = 35 \) ways.
   - After assigning 3 people, we have 4 people left. We need to assign 2 people to one vehicle and 2 to the other.
   - The number of ways to split these 4 people into two groups of 2 is \( \frac{\binom{4}{2}}{2!} \). We divide by \( 2! \) because the two groups of 2 are indistinguishable. This gives \( \frac{6}{2} = 3 \) ways.

5. **Step 4: Total number of ways:**
   The total number of ways to distribute the 7 people into the 3 vehicles is \( 35 \times 3 = 105 \).

However, upon review, we need to adjust for ordering of vehicles and revisit combinatorics for constraints,

7 people visited a marriage function in 3 different vehicles, each accommodating a maximum of 5 persons. In how many ways can they visit, such that they use all the 3 vehicles?

Solve a combinatorics problem involving the distribution of 7 people into 3 vehicles, ensuring each vehicle is used and carries at least 1 person. The solution uses concepts like combinations, permutations, and the stars and bars method. Ideal for high school students studying combinatorics.

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