Would the following code achieve the goal?
var random:int = Math.floor(Math.random() * 10) + 1;
Basically Math.random() would generate a number from 0 to 1 (1 excluded), multiply the result from Math.random() would return a number from 0 to 10 (but 10 is excluded).
By doing a Math.floor, that would result a random number from 0 to 9, so adding 1 to it would then result a random number from 1 to 10.