Lets define the positions as 1 through 9. We want to choose 4 positions such that no two are adjacent.

March 11, 2026

Lets define the positions as 1 through 9. We want to choose 4 positions such that no two are adjacent.

**Lets define the positions as 1 through 9. We

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Favorable outcomes for all dice different:
So, probability that all dice are different:
Question: A GIS analyst is analyzing satellite data from 9 time points and wants to select 4 non-consecutive time intervals for detailed heat zone analysis. How many ways can she choose 4 non-consecutive time points from the 9?
This is equivalent to choosing 4 positions from 9 such that there is at least one gap between any two selected positions.
To model this, imagine placing 4 selected positions (denoted S) and 5 unselected positions (denoted U), such that no two Ss are adjacent.
To ensure non-consecutiveness, we must place at least one U between each pair of Ss. That is, we place 3 Us to separate the 4 Ss.

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