Four tires to mount on a car these can be mounted

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    Car Tires
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Discussion Overview

The discussion revolves around the different ways to mount four tires on a vehicle, exploring combinatorial reasoning and the assumptions behind different calculations. Participants examine the implications of tire selection based on vehicle type, specifically contrasting two-wheeled and three-wheeled vehicles.

Discussion Character

  • Exploratory, Mathematical reasoning, Conceptual clarification

Main Points Raised

  • One participant asserts that four tires can be mounted in 4! (24) different ways, questioning an initial assumption of 4*4 (16) ways.
  • Another participant explains the reasoning behind the 4! calculation, detailing the decreasing number of choices for each subsequent tire.
  • A participant queries the necessity of a two-wheeled vehicle for the 4*4 calculation, suggesting that if there were three wheels, the calculation might be 4*4*4.
  • Another participant agrees with the multiplication approach for a three-wheeled vehicle, indicating that each tire could be independently chosen from four options.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the 4*4 calculation, with some supporting it for specific vehicle types while others challenge its relevance to the original problem of mounting four tires on a four-wheeled vehicle. The discussion remains unresolved regarding the conditions under which each calculation applies.

Contextual Notes

The discussion highlights assumptions about vehicle types and the independence of tire choices, which may not be universally applicable. The relationship between the number of tires and the number of wheels on a vehicle is a key factor in the calculations presented.

TSN79
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If you have four tires to mount on a car these can be mounted in 4!=24 different ways. I initially thought it would be 4*4=16 ways. Why is this assumption wrong? What would the problem have to be like for my 4*4 to be the solution?
 
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Four different tires can be mounted in 4! ways because you have 4 possibilities for the first wheel, then only 3 for the second wheel (since the tire you put on the first wheel can't be put on the second wheel) then only 2 possibilities for the third one and then only 1 for the last.

An example of 4 * 4 = 16 ways is if you have 4 different types of tires and large numbers of each type, and a two-wheeled vehicle, then you have 4*4 = 16 different ways to choose your tires.
 
Hmm...if I have four brands of tires, that would explain the first 4-digit, but how come the vehicle has to be two wheeled...? If the vehicle had three wheels, would the answer then be 4*4*4 ?
 
Yes-four possibilities for the type of each tire, so you multiply them together. 4*4 for a two-wheeled vehicle, 4*4*4 for a three-wheeled vehicle.
 

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