Determine the number of 10-digit decimal numbers such that the digits that are odd are increasing from left to right, and the digits that are even are decreasing from left to right.
Let's see here...
The odd digits must be going 1,3,5,7,9
The even: 8,6,4,2,0
Normally, there would be 10! ways to arrange it, but we must divide by 5!^2 because there is only one way to arrange even and odds. Therefore there are 252 numbers.