Oh man, my apologies for not noticing this. Your equation doesn't take natural selection into count. Evolving doesn't access require every combination of DNA. Not even close. All that is required are the combinations that work. Natural selection causes this to happen very rapidly, as the creatures with only the most advantageous DNA combinations survive, creating an already established combination to build from for the next generation. The math isn't as you say.
I believe in evolution so fare as it's the best answer science has. Also there is far more evidence for evolution as their is for the existence of any specific God.
The sign argument is strange to me, especially if the sign is something as common place as a shooting star.
Why would god allow you to prove his existence? Well that depends on the God. If we are talking a Chritian/Muslim god like this meme, than it would be pretty damn immoral to send billions of people to hell for not believing in what hasn't been shown to exist.