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asdfghjkl13
31-07-2017
Mathematics
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Combinations- how to show that 10C2=10C8
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LammettHash
LammettHash
31-07-2017
By definition,
[tex]{}^nC_k=\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]
We have
[tex]\dbinom{10}2=\dfrac{10!}{2!(10-2)!}=\dfrac{10!}{2!8!}=\dfrac{10!}{(10-8)!8!}=\dbinom{10}8[/tex]
and so
[tex]{}^{10}C_8={}^{10}C_2[/tex]
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