FactorialIn mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book Sefer Yetzirah.
CombinationIn mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members.
VestigialityVestigiality is the retention, during the process of evolution, of genetically determined structures or attributes that have lost some or all of the ancestral function in a given species. Assessment of the vestigiality must generally rely on comparison with homologous features in related species. The emergence of vestigiality occurs by normal evolutionary processes, typically by loss of function of a feature that is no longer subject to positive selection pressures when it loses its value in a changing environment.
