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**Is there a way to do this without "brute force"?**

## Homework Statement

A number is chosen at random from among all 5-digit numbers containing exactly one of each of the digits 1, 2, 3, 4, 5. Find the probability that no two adjacent digits in the number are consecutive integers?

## Homework Equations

n choose k

n factorial

## The Attempt at a Solution

So I know there are 5!=120 different combos. I need to figure out how many have the property that there are no two adjacent consecutive numbers (i.e. 13524 would work but 12534 wouldn't). Should I break it off into cases where 1 is the first digit, 2 is the second, etc.? That would be a brute force approach. Is there an easier way to think about this?

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