Is there a way to do this without "brute force"? 1. The problem statement, all variables and given/known data 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? 2. Relevant equations n choose k n factorial 3. 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?