Suppose, as a rough estimate, we say that there are 20 distinct geons used for object recognition; and each geon can come in 5 classifiable qualitative sizes (tiny, small, moderate, large, huge); and a pair of geons can be placed in 10 distinct qualitative relations (geon A on top of geon B; geon A to upper left of geon B; geon A to the left of geon B; and so forth). How many distinct two-geon objects do we have in the space described above?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 10AEXP
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  1. Suppose, as a rough estimate, we say that there are 20 distinct geons used for object recognition; and each geon can come in 5 classifiable qualitative sizes (tiny, small, moderate, large, huge); and a pair of geons can be placed in 10 distinct qualitative relations (geon A on top of geon B; geon A to upper left of geon B; geon A to the left of geon B; and so forth).

How many distinct two-geon objects do we have in the space described above?

 

2.Now, suppose we add a third geon, geon C. Again, each geon comes in 20 varieties and 5 sizes. We'll start by creating a two-geon pair of A and B just like in Question 1 above; then, we decide which of A or B the third geon (C) will be adjacent to, and then we place geon C beside either A or B in one of the 10 allowed relations. How many distinct three-geon objects do we have in this space?

Note:Both 1 & 2 Questions are interrelated.I request you to answer both:

Note;Earlier answers given by experts are as below which are wrong:

49,500,

19!

19!x19!

1.2*10^17

1000

250

150.

All above answers are wrong.Please suggest the right answer

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