Sigh. Again and again Creationists make this simplistic fallacy, again and again their mistake is pointed out to them and explained in detail.
Then they make it again.
All you've computed is the odds of N specific mutations occurring *in a row*, with *no other mutations occurring*.
Sure, that would be practically impossible, mathematically enormous odds.
However, your mistake is in assuming that the "N" mutations have to happen one after the other without fail, bam-bam-bam.
This is *not* what evolution postulates, AT ALL. Therefore, your result has absolutely nothing to do with the actual likelihood of successful evolution. It's just mathematical masturbation.
Instead, evolution postulates that somewhere, among thousands or millions of individuals in a population, amid countless other mutations occurring within the population during reproduction, beneficial mutation "N1" happens to occur.
Your calculation includes a term (P1) for N1 happening, FIRST TRY, AND NOTHING ELSE BEING ALLOWED TO OCCUR (which is of course highly unlikely). This is where you make your first major error.
Instead, you need to calculate the odds of mutation N1 happening, *at all*, over a huge number of individuals, across a large number of generations. This is, needless to say, much less unlikely. In fact, over sufficient time, it approaches certainty.
Then, your calculation presumes that mutation P2 must happen ON THE VERY NEXT MUTATION EVENT. This is, again, highly unlikely. But that's not what evolution postulates, so that's your error #2.
Instead, you simply need to calculate the odds of mutation P2 happening *sometime* in the future, to *any* of the countless generations of offspring which happen to inherit mutation N1 from the original individual in which it occurred. Note that it doesn't have to be the very next mutation event, as you presume, it could happen in the fortieth generation, among any one of thousands of descendants, after 100,000 other mutations had occurred within the population.
Again, note how much more likely this is than your presumption that the "N" mutations must occur *exclusive* to any other.
And so on through the rest of the N mutations.
If you're going to use math to analyze something, please be sure you first understand the process you're attempting to model.
Class dismissed.
Only fools would argue constantly about something they don't have a shred of proof for.
Evolutions are fools and freepers need not waste their time with them. They are irrelevant.
For the math in this thread, when we are dealing with useful data, the information actually does have to sequence itself one after the other to make the final output. Whether we are dealing with monkeys accidentally typing a sentence from Shakespeare, software programs self-forming on your hard drive after a lightning strike, or DNA bases creating a double-helix structure with the proper codes to create Life, the sequence really does matter. Re-order a few 1's and 0's in a softwre program, re-order a few characters in a sentence, or re-order the bases in a gene and the final desired output will no longer be achieved.
"Instead, you need to calculate the odds of mutation N1 happening, *at all*, over a huge number of individuals, across a large number of generations. This is, needless to say, much less unlikely. In fact, over sufficient time, it approaches certainty." - Dan Day
Actually, for what you are proposing, you would need to first calculate the odds of mutation N1 happening at all, then second the odds of life-form with mutation N1 surviving, then propagating, then finally of said mutation N1 appearing succesfully in offspring.
There are lots of observable mutations. Two-headed snakes are one such example, for instance, yet how often do two-headed snakes survive, much less propagate, much less have said mutation successfully appear in their offspring?
A mutation can usually be considered to be a mistake in genetic code copying. Can we see mistakes in said copying after they've occured? Yes. Is that the same as seeing the mutation/mistake propagate? No.
So for the math that you propose above to be valid, one would to need make Additional calculations than the single equation you alluded to above.
Although it would usually go without saying, considering the behavior on this thread it is probably worth pointing out that those additional calculations will greatly lower the probability of such events.
Now, would a lower probability matter in an infinite universe with an infinite amount of time? No.
Do we live in an infinite universe with an infinite amount of time? No.
Which means, of course, that the lower probability matters.