To explain: why the combination binom{n}{r}=binom{n}{r,n-r}.

banganX 2020-12-30 Answered

To explain: why the combination (nr)=(nr,nr)

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Expert Answer

yagombyeR
Answered 2020-12-31 Author has 92 answers

Formula used:
The number of combinations of choosing r objects from n objects is
{n}Cr=n!(nr)r!
The number of combinations of choosing two groups x and y from n objects is
{n}Cx,y=n!x!y!(nxy)!
Consider the number of combinations of choosing r objects from n objects =(nr)
Let n is divided in to two groups one is having r objects and other group is having n
(nr) Objects, that is n=r+(nr), then
The number of ways of Choosing two groups r and n  r from n objects =(nr,n  r)
(nr,nr)=n!r!(nr)!(n(nr)r)!
=n!r!(nr)(nn+rr)
=n!r!(nr)!
=(nr)
Therefore, (nr)=(nr,nr)
Hence, explained

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