Show that: nCr = n-1Cr + n-1Cr-1 ??

1 Answer
Mar 24, 2018

See the proof below

Explanation:

This is the proof of the Pascal's Triangle

RHS=((n-1),(r))+((n-1),(r-1))

=((n-1)!)/((n-r-1)!(r)!)+((n-1)!)/((n-r)!(r-1)!)

=(n-1)!(1/((n-r-1)!(r)!)+1/((n-r)!(r-1)!))

=(n-1)!((n-r)/((n-r)(n-r-1)!(r)!)+r/((n-r)!r(r-1)!))

=(n-1)!((n-r)/((n-r)!(r)!)+r/((n-r)!(r)!))

=(n-1)!*n/((n-r)!(r)!)

=(n!)/((n-r)!(r)!)

=((n),(r))

=LHS

QED