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Show that if $n$ is a positive integer, then $1 = \binom{n}{0}<\binom{n}{1}<\dots < \binom{n}{\left \lfloor n/2 \right \rfloor} = \binom{n}{\left \lceil n/2 \right \rceil}>\dots \binom{n}{n-1}>\binom{n}{n}=1.$
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we are taking n=9

C(9,0)=9!/9!0!=1

C(9,1)=9!/1!8!=9

C(9,2)=9!/2!7!=36

C(9,3)=9!/3!6!=84

C(9,4)=9!/4!5!=126

C(9,5)=9!/4!5!=126

C(9,6)=9!/3!6!=84

C(9,7)=9!/2!7!=36

C(9,8)=9!/1!8!=9

C(9,9)=9!/9!0!=1

here you can see

1,9,36,84,126,126,84,36,9,1

1=C(9,0)<C(9,1)<C(9,2)<C(9,3)<C(9,4)=C(9,4)>C(9,6)>C(9,7)>C(9,8)>C(9,9)=1

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