Solve Travel Problem: 10 Fans in 3 Taxis

  • Context: Undergrad 
  • Thread starter Thread starter Gotcha
  • Start date Start date
Click For Summary
SUMMARY

The problem of transporting 10 fans in three taxis with capacities of 2, 4, and 5 passengers respectively can be solved using combinatorial methods. The key configurations identified include placing 2 fans in Taxi 1, 4 in Taxi 2, and 4 in Taxi 3, among other combinations. The analysis confirms that there are three distinct ways to allocate the fans given the constraints of the taxi capacities and the total number of fans. This conclusion is based on the principle of distributing the spare seat across the taxis.

PREREQUISITES
  • Combinatorial mathematics
  • Understanding of permutations and combinations
  • Knowledge of binomial coefficients
  • Basic principles of normal distributions
NEXT STEPS
  • Study advanced combinatorial techniques for complex distribution problems
  • Learn about generating functions in combinatorics
  • Explore the application of the multinomial theorem
  • Investigate real-world applications of combinatorial optimization
USEFUL FOR

Students preparing for exams in combinatorial mathematics, educators teaching permutations and combinations, and anyone interested in solving distribution problems in logistics.

Gotcha
Messages
11
Reaction score
0
Here is a problem that I need to solve in preparation of my exams
(I know how to use combinations, permutations, binomial coeeficcients, normal distributions):

Ten fans are traveling to a rugby match in three taxis that will hold 2, 4 and 5 passengers respectively. In how many ways is it possible to transport the 10 people to the rugby match.
:confused:
 
Physics news on Phys.org
1st 2 in taxi1 4 in Taxi2 and 4 in taxi3
2nd 2 in Taxi1 5 in taxi3 and 3 in Taxi2
3rd 1 in taxi1 5in taxi3 and 4 in taxi2
so there are 3 possible ways...thats because you have only one spare seat in all three taxis so the spare seat can be in all three taxis
 

Similar threads

High School How to solve factorial related problems
  • · Replies 4 ·
Replies
4
Views
4K
Maximizing Revenue: Solving a Probability Problem in Statistics and Probability
  • · Replies 3 ·
Replies
3
Views
2K
I need help, please, designing a pool sensor for breaking . . .
  • · Replies 2 ·
Replies
2
Views
2K
Solve the Statistics Problem: 10 Paintings to 3 Heirs
  • · Replies 6 ·
Replies
6
Views
9K
Programs How good is this applied math program?
  • · Replies 13 ·
Replies
13
Views
4K
Comp Sci Solve C++ & ROOT Problems: 3 Questions Answered
  • · Replies 8 ·
Replies
8
Views
2K
Solving energy and food problems as a career
  • · Replies 16 ·
Replies
16
Views
7K
Undergrad Atmospheric Density vs Altitude in an O'Neil Cylinder
  • · Replies 1 ·
Replies
1
Views
3K
Challenge Math Challenge - April 2020
  • · Replies 150 ·
6
Replies
150
Views
22K
Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)
  • · Replies 2 ·
Replies
2
Views
2K