A four-digit number is selected at random. What is the probability that its ones place is greater than its tens place, its tens place is greater than its hundreds place, and its hundreds place is greater than its thousands place? Note that the first digit of an n-digit number is nonzero.

To find the probability, we need to determine the number of favorable outcomes (numbers that satisfy the given condition) and the total number of possible outcomes (all four-digit numbers where the first digit is nonzero).

First, let's identify the possible values for each place value:

- Thousands place: It can take any value from 1 to 9.
- Hundreds place: Since it must be greater than the thousands place, it can take any value from 2 to 9.
- Tens place: It must be greater than the hundreds place, so it can take any value from 3 to 9.
- Ones place: It must be greater than the tens place, so it can take any value from 4 to 9.

Now, let's find the favorable outcomes. We need to find the number of four-digit numbers that satisfy the given conditions.

For the thousands place, there are 9 possible values (1 to 9).

For the hundreds place, there are 7 possible values (from 2 to 9, excluding the value chosen for the thousands place).

For the tens place, there are 5 possible values (from 3 to 9, excluding the values chosen for the thousands and hundreds places).

For the ones place, there are 4 possible values (from 4 to 9, excluding the values chosen for the thousands, hundreds, and tens places).

To calculate the total number of favorable outcomes, we multiply the number of possibilities for each place: 9 x 7 x 5 x 4 = 1,260.

Now, let's find the total number of possible four-digit numbers where the first digit is nonzero.

The thousands place can have 9 possible values (from 1 to 9).

The hundreds place can have 9 possible values (from 0 to 9, excluding the value chosen for the thousands place).

The tens place can have 9 possible values (from 0 to 9, excluding the values chosen for the thousands and hundreds places).

The ones place can have 9 possible values (from 0 to 9, excluding the values chosen for the thousands, hundreds, and tens places).

To calculate the total number of possible outcomes, we multiply the number of possibilities for each place: 9 x 9 x 9 x 9 = 6,561.

Therefore, the probability of selecting a four-digit number that satisfies the given conditions is 1,260/6,561 = 0.192 or 19.2%.

So, the probability is approximately 0.192 or 19.2%.