I am a little confused at how to solve the Permutations

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Homework Help Overview

The problem involves determining the number of ways to arrange five distinct Martians, ten distinct Vesuvians, and eight distinct Jovians in a line, with the condition that no two Martians stand together. The complexity arises from the inclusion of multiple groups of distinct individuals.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of having multiple groups and how that affects the arrangement of Martians. There is a suggestion to consider the total number of distinct individuals as a single group of "ALIENS" and to explore how to position the Martians among them.

Discussion Status

The discussion is ongoing, with participants questioning the validity of their calculations and exploring different interpretations of how to approach the problem. Some guidance has been offered regarding the arrangement of the distinct groups and the placement of Martians, but no consensus has been reached.

Contextual Notes

Participants are grappling with the constraints of the problem, particularly the requirement that no two Martians can stand together, and how to effectively account for the distinct groups involved in the arrangement.

Bucs44
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I am a little confused at how to solve the following problem:

In how many ways can five distinct Martians, ten distinct Vesuvians, and eight distinct Jovians wait in line if no two Martians stand together?


What is throwing me off is the addition of another group - if it was just Martians and Vesuvians it would be easy. My guess is P(10,5) = (10*9*8*7*6)

Am I correct or did I mess this up?
 
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It doesn't matter how the Vesuvians and Jovians stand so thinking of these as ALIENS you DO have two groups 5 Martians and 18 ALIENS
 
So my calculation was wrong? It should be P(18,5) ?
 
How many ways could you arrange the ALIENS? Remember they are all distinct.

How many ways could you then slot in the Martians to meet the conditions?
 
Right - Because there are 18 Vesuvians and Jovians, the Martians can either fit in the front of the line, middle or end of the line. In which case there would be 19 spots where they could fit in line. P(19,5) = 1,395,360
 
Bucs44 said:
Right - Because there are 18 Vesuvians and Jovians, the Martians can either fit in the front of the line, middle or end of the line. In which case there would be 19 spots where they could fit in line. P(19,5) = 1,395,360

Is this right?
 

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