Editing Binomial theorem (section)

=== Combinatorial interpretation ===
The binomial coefficient <math> \tbinom nk </math> can be interpreted as the number of ways to choose {{mvar|k}} elements from an {{mvar|n}}-element set (a [[combination]]). This is related to binomials for the following reason: if we write {{math|1=(''x'' + ''y'')<sup>''n''</sup>}} as a [[Product (mathematics)|product]]
<math display="block">(x+y)(x+y)(x+y)\cdots(x+y),</math>
then, according to the [[distributive law]], there will be one term in the expansion for each choice of either {{mvar|x}} or {{mvar|y}} from each of the binomials of the product. For example, there will only be one term {{math|''x''<sup>''n''</sup>}}, corresponding to choosing {{mvar|x}} from each binomial. However, there will be several terms of the form {{math|''x''<sup>''n''−2</sup>''y''<sup>2</sup>}}, one for each way of choosing exactly two binomials to contribute a {{mvar|y}}. Therefore, after [[combining like terms]], the coefficient of {{math|''x''<sup>''n''−2</sup>''y''<sup>2</sup>}} will be equal to the number of ways to choose exactly {{math|2}} elements from an {{mvar|n}}-element set.