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## Random Numbers with Constraints

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #14704 Fun: (2.18) Difficulty: (2.11) Category: Probability Submitted By: j72883 Corrected By: Winner4600

Generate two random numbers from 1 to 9, inclusive. Call them n1 and n2. What is the probability that | n1 - n2 | > 5?

### Answer

12/81

Since you are making two choices of 9 numbers each, there are 81 total possible combinations (9 x 9).

The only combinations that have a difference greater than 5 are:

9 and 1, 2, or 3
8 and 1 or 2
7 and 1

This makes six combinations, but you also have to take them in the reverse order (i.e. 1 and 9 is a different combination than 9 and 1). This makes a total of 12 possibilities, making the probability 12 in 81.

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