Is it possible to solve this using the FCP rule?
Yes, it's possible to use the Fundamental Counting Principle here:
The probability = (number of ways that satisfy condition) / (total number of ways)
The numerator is just 1; there is only one way to choose the four numbers in ascending order: 1, 2, 3, 4
We use the FCP to find the denominator, the total number of ways. We have 4 choices for the first number, 3 for the second, 2 for the third, 1 for the last:
So our total ways is 4 * 3 * 2 *1 = 24
So our probability is 1/24