Calculating Probability of "Lucky" Bus Riders in a City

[chocolatefrog]

"Bus tickets in a certain city contain four numbers, U, V, W, X. Each of these four numbers is equally likely to be any of the ten digits 0, 1, 2,...,9 and the four numbers are chosen independently. A bus rider is said to be lucky if U + V = W + X. What proportion of the bus riders are lucky?"

I tried calculating the numerator, but there are just so many possibilities, what with repetition of digits! Needless to add, I couldn't get to the answer. :| I was wondering if there's a simple, more elegant way of doing this.

Thanks in advance!
Regards.

 

[Valkarie]

The proportion of lucky bus riders is 1/10, since for every 10 combinations, there will be one combination where U + V = W + X.