Week 1 DQ 1 Response
1) Given the enumeration methods; sum rule, product rule, permutations, combinations along with enumeration methods for indistinguishable objects, how can we devise a strategy to solve problems requiring these methods?

A basic concept in the branch of the theory of algorithms called enumeration theory, which investigates general properties of classes of objects numbered by arbitrary constructive objects (cf. Constructive object). Most often, natural numbers appear in the role of the constructive objects that serve as numbers of the elements of the classes in question ("Enumeration", 2013).
The Sum/Difference Rules refer to the derivative of the sum of two functions is the sum of the derivatives of the two functions ("Basic Derivative Rules", 2013).
The product rule is one of several rules used to find the derivative of a function. Specifically, it is used to find the derivative of the product of two functions. It is also called Leibnitz's Law, and it states that for two functions f and g their derivative (in Leibnitz notation, ). The derivative of f times g is not equal to the derivative of f times the derivative of g: .The product rule can be used with multiple functions and is used to derive the power rule. The product rule can also be applied to dot products and cross products of vector functions. The Leibnitz Identity, a generalization of the product rule, can be applied to find higher-order derivatives ("Definition Of Product Rule", 2013).
A permutation in mathematics is one of several ways of arranging or picking a set of items. The number of permutations possible for arranging a given a set of n numbers is equal to n factorial (n!). So, a set of three numbers can be arranged as: 3x2x1 = 6 permutations ("Permutation", 2013).
A Combination is a selection of some or all of a number of different objects. It is an un-ordered collection of