The Binomial Expansion
We can use the binomial theorem to expand and simplify expressionsof the form
where
isany positive whole number.
The general expansions is
Example:
The coefficients gere have a special signifucance.
isthe number of ways in which a term with 
canbe generated when
isexpanded fully.
Suppose we have 5 men of which three are to be selected forpromotion. The number of ways in which three men can be selected fromthe five is the same
generatedby the binomial expansion above. When choosing a selection of
froma possiblewesay 'choose'We may write it as
or
Given a set ofindividuals,the total number of selections of any size that can be made is
Thiscan also be deduced from the binomial theorem.
The total number of selections of size 0 is
The total number of selections of size 1 is
The total number of selections of size 2 is
The total number of selections of size
is
The total number of selections of size n is
Adding all these up gives
andwe can write this as
