A“descending number” is a three-digit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. what is the probability that a three-digit number chosen at random is a “descending number”?

Fix the first digit to be 2. How many two-digit descending numbers can you make? Only one, and that would be .

Now fix the first digit to be 3. How many two-digit descending numbers can you make? There are three, and these are .

Next, if the first digit is 4, then there are six possible descending numbers, .

You might start seeing a pattern here. If the first digit is , then each choice of from contributes more possible two-digit permutations that are descending.

As the pattern continues, you'll find that the total number of descending three-digit numbers is



Meanwhile, there are possible three-digit numbers that can be randomly chosen (100 through 999), so the probability you're looking for is .