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Let n\ a n d\ r be non negative integers...

Let `n\ a n d\ r` be non negative integers such that `1lt=rlt=ndot` Then, `\ ^n C_r=n/rdot\ \ ^(n-1)C_(r-1)\ dot`

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`\ ^n C_r=n/rdot\ \ ^(n-1)C_(r-1)\ dot`
RHS=`n/rdot\ \ ^(n-1)C_(r-1)\ dot`
=`n/r*(n-1)!/(r-1)!*(n-1)-(r-1)!`
=`n/r*(n-1)!/(r-1)!*1/(n-1)-(r-1)!`
=`\ ^n C_r`
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