PROVE THAT nPr=n-1Pr+rn-1Pr-1
THIS IS ONLY FOR WHO ARE IN 11 CLASS,
PLEASE DON'T ANSWER OTHERS
Answers
Answered by
9
R.H.S
(n-1)!/(n-1-r)!+r.(n-1)!/(n-r)!
=(n-1)!/(n-r-1)!+r.(n-1)!/(n-r)(n-r-1)!
=(n-1)!/(n-r-1)!+(1+r/n-r)
=(n-1)!/(n-r-1)!(n/n-r)
=n!/(n-r)!
=nPr
(n-1)!/(n-1-r)!+r.(n-1)!/(n-r)!
=(n-1)!/(n-r-1)!+r.(n-1)!/(n-r)(n-r-1)!
=(n-1)!/(n-r-1)!+(1+r/n-r)
=(n-1)!/(n-r-1)!(n/n-r)
=n!/(n-r)!
=nPr
Attachments:
Similar questions