Math Problem Statement
7 people visited a marriage function in 3 different vehicles, each accommodating a maximum of 5 persons. in how many ways can they set, sach that they use of the vehicles
Pick ONE option
3600
1500
1650
1806
Solution
We are given 7 people who need to be seated in 3 vehicles, with each vehicle accommodating a maximum of 5 persons. The goal is to find how many ways they can be seated in such a way that all vehicles are used.
Step-by-step breakdown:
- Total number of people: There are 7 people in total.
- Distribution of people across vehicles: We must ensure that all 3 vehicles are used, so the possible distribution of people across the vehicles can only be . This is because each vehicle can hold up to 5 people, and the other two must have at least one person to satisfy the condition that all vehicles are used.
Steps to solve:
- First, choose which vehicle will have 5 people. This can be done in ways (since we are selecting 1 vehicle out of 3).
- Now, out of 7 people, choose 5 to go into the selected vehicle. This can be done in ways.
- The remaining 2 people will be divided between the other two vehicles. Since each of these vehicles will get exactly 1 person, the number of ways to assign 1 person to each vehicle is .
Total number of ways:
Finally, the correct option provided is not listed based on these calculations.
The calculation might miss the specific options listed
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations
Combinations
Formulas
Combination formula: \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \)
Factorial formula: n! = n × (n-1) × ... × 1
Theorems
-
Suitable Grade Level
Grades 9-12
Related Recommendation
How to Arrange 7 People in 3 Vehicles Using Combinatorics
Arranging 7 People in 3 Vehicles Using Combinatorics and Permutations
Combinatorial Solution for Distributing 7 People in 3 Vehicles
Combinatorics Problem: Distributing 7 People Across 3 Vehicles
Combinatorics Problem: Distributing 7 People Across 3 Vehicles