I think you have to try and define the word random within the context of evolution (versus creation). I'm not a scientist but do believe in a form of evolution - species fighting for dominance to ensure their genes are carried on - there's just too much evidence to ignore isn't there? -but there have to be failings or exceptions within this theory and this is where the idea of random events occur. Evolution is still working itself out!
Isn't it basically an instinct versus intelligence question? Darwin studied finches to back up his theory and concluded that specialist features in certain birds meant that they had evolved to suit their environment so they could feed and breed and survive. How these changes occur within the genetic make up is so difficult to pinpoint. Change of feature equals better opportunity to sustain successful genes so the actual physical changes in a finch say, (could be a finer tuned bill or some subtle colouring for camouflage) come about through time and molecular nuances within the DNA?
So you might start off with 10 sub-species of finch and over millions of years narrow it down to 1 or 2 survivors who have evolved a thinner beak to get the seeds and the colouring to avoid being detected by potential enemies.
The randomness happens when these tiny changes are taking place - due to all the different factors involved: environment, behaviour, chance meetings, unpredictable events in weather, change in food source and so on.
I think we need a flexible approach to the theory of Darwinism. There may be mathematical laws at work on one level but there is also the butterfly effect to consider at sub-atomic level - and that is another different kettle of fish completely.