Editing Binomial theorem (section)

=== Multinomial theorem ===
{{Main|Multinomial theorem}}
The binomial theorem can be generalized to include powers of sums with more than two terms. The general version is

<math display="block">(x_1 + x_2 + \cdots + x_m)^n = \sum_{k_1+k_2+\cdots +k_m = n} \binom{n}{k_1, k_2, \ldots, k_m} x_1^{k_1} x_2^{k_2} \cdots x_m^{k_m}, </math>

where the summation is taken over all sequences of nonnegative integer indices {{math|''k''<sub>1</sub>}} through {{math|''k''<sub>''m''</sub>}} such that the sum of all {{math|''k''<sub>''i''</sub>}} is&nbsp;{{mvar|n}}. (For each term in the expansion, the exponents must add up to&nbsp;{{mvar|n}}). The coefficients <math> \tbinom{n}{k_1,\cdots,k_m} </math> are known as multinomial coefficients, and can be computed by the formula
<math display="block"> \binom{n}{k_1, k_2, \ldots, k_m} = \frac{n!}{k_1! \cdot k_2! \cdots k_m!}.</math>

Combinatorially, the multinomial coefficient <math>\tbinom{n}{k_1,\cdots,k_m}</math> counts the number of different ways to [[Partition of a set|partition]] an {{mvar|n}}-element set into [[Disjoint sets|disjoint]] [[subset]]s of sizes {{math|1=''k''<sub>1</sub>, ..., ''k''<sub>''m''</sub>}}.