Natural selection is a machine that makes almost impossible things. Consider a typical protein such as whale myoglobin. That molecule is but one of a hundred thousand or so proteins in the animal’s body and contains a hundred and fifty-three units called amino acids. These come in about twenty forms. The number of possible combinations of amino acids in a structure the size of myoglobin is hence twenty raised to the power of a hundred and fifty three. The figure, ten with about two hundred zeros after it, is beyond imagination and is far more than all the proteins in all the whales, all the animals and all the plants that have ever lived. Such a molecule could never arise by accident. Instead, a rather ordinary device, natural selection, has carved out not just myoglobin but millions of other proteins and the organisms they build.
Look up “protein domains” and “cumulative selection” to find out why the model used to calculate the probability is wrong.