After all, if any possible gene will occur, and once having occurred will never disappear, then there is really no selection.

I think you misunderstood, It is the very process of selection that causes the preservation. Separating the genes that cause themselves to be reproduced from those that do not is the very essence of natural selection. The vast majority of mutations get “forgotten” because they don’t help duplicate themselves. Once a gene does lead to its own duplication (by helping the organism of which it is a part) then natural selection will give it a place at the expense of those other genes who did not. However, once the gene no longer leads to its own duplication, then natural selection “forgets” and the gene starts to fade way.

I take it that success here means stumbled upon a mechanism that allows the cancer cell to survive and reproduce itself outside the original host. But then, that seems to mean that trillions of mutated cancer cells failed, and presumably many of these failures enjoyed unique genetic combinations.

Yes, but being unique doesn’t count. Only being “right” counts. All cancers evolve. Most cancers result from multiple genetic mutations which occur in a series. For each cell whose decedents eventually become a threatening cancer, hundreds of millions die along the way due either to fatal mutation or the bodies anti-cancer defenses.

Its best to think of natural selection as operating like a peg and peg board system. The peg change randomly. If they fit a hole in the peg board, they get copied. Eventually, all the pegs (except those that just mutated) will have shapes that fit them into holes on the board. Change the shape of holes however, and the process starts all over again.

Either natural selection does not occur at all, or the second statement there is false. After all, if any possible gene will occur, and once having occurred will never disappear, then there is really no selection. This also seems to contradict earlier statements, for instance: “Of all the trillions of cancer cells that mutate each year in every multicellular species on earth, we know of only this one that has succeeded at some time in the last 1000 years.” I take it that success here means stumbled upon a mechanism that allows the cancer cell to survive and reproduce itself outside the original host. But then, that seems to mean that trillions of mutated cancer cells failed, and presumably many of these failures enjoyed unique genetic combinations. Actually, the thrust of the piece appears to be that the odds against any particular gene or combination of genes happening to be reproductively successful are enormous, but it does happen, and often in astonishing ways.