On randomness
The basic argument goes like this:
The Earth and the life on it are complex, it's impossible for complexity to come from randomness, therefore a creator is needed.
The more "advanced" of these people will have heard of the second law of thermodynamics and in a complete misunderstanding of the law state that randomness can't create order, but that is another post entierly.
They are taking the fact that there is a small amount of random chance in the system to basically state that if you take all the particles in the universe, give them a shake, then the odds of coming up with us is so small as to be impossible. Now if the system were completely random, then this would be true. The problem is that they don't understand that the stochastic processes in the universe are all constrained by the laws of physics.
By way of analogy I will use the Canadian national lottery 6/49. In this lottery a machine is loaded with 49 balls numbered 1 to 49. Six are drawn at random from the machine. If the six numbers you have entered match the drawn numbers you are financially well off. Now the game is predicated in that it's next to impossible to predict what six balls will come out at any time. To be logically consistent using their randomness argument, the creationist would have to argue that it was impossible to win the lottery. Since people win the lotto all the time, this is obviously wrong. Why?
The reason is that the randomness in the lottery is constrained. There are a large but limited number of outcomes. There are only 13 983 816 unique combinations of winning numbers. Further it can be stated with near certainty that, if using the set of natural numbers, numbers greater than 49 will not be spewing forth from the machine. Nor will other symbols. So a completely random game is actually severely constrained. Not just anything can happen. Three balls and four sugar cubes numbered 75 through 83 will not be coming out of the machine. One can even make predictions on the game. For example it can be predicted that at least once in every 14 million plays, there will be at least one winner. Though that seems next to impossible since for any particular player the odds are long, when millions of people play every draw, it only takes a couple of weeks, on average, for someone to win. The reality is that probability is a well understood branch of mathematics. So well understood that Casinos make a mint off of it.
The universe is the same way. Though randomness is in the universe, it is severely constrained. For example if one looks at the periodic table, the number of diatomic (two element) combinations of natural elements possible if any two of the 98 naturally occurring elements were to combine is 4753 combinations. Not a lot of combinations, but we're only looking at diatomic molecules, but bear with me. Since the game is constrained only certain combinations are permitted. For example metals never bond with other metals, iron nicklide can't happen. Further the noble gasses don't form compounds under normal conditions taking six elements out of the mix completely. With just these two constraints the number of combinations drops to 1380, considerably less. This holds true for larger molecules as well as further constraints get added with each atom and type of atom. A single carbon atom can bond with at most 4 other atoms for example.
These constraints on chemical bonds limit the combinations of elements that are allowed to form compounds. They also constrain how these compounds interact with each other. In other words the odds of the compounds of life arising from "random" processes are actually pretty good given the vastness of the universe, because as with the national lotto, the randomness is severely constrained.
Now at this point a particularly bright creationist might ask "but who's doing the constraining" and then posit a deity (usually some form of the Abrahamic god) as the constrainer. They will completely ignore the fact that the laws of physics are what are doing the constraining. Further not all "random" processes are even random. Though random mutation is one factor in helping evolution along, it is natural selection in response to changes in the environment that is the driving force. Though it's not possible to predict what changes will happen, it is possible to state that change will happen. Either by adaptation, genetic or behavioural, or by the organism going extinct. Same goes for abiogenesis and planet formation, constraints on both "random" processes either by chemistry or gravity will tend the process to a small number of possible outcomes.
So if a creationist starts spouting off "randomness" as preventing, well anything, rest assured in the knowledge that they don't understand, physics, chemistry, biology or even probability mathematics. But you probably knew that already.