Show that `^nP_r=(n-r+1)^nP_(r-1)`

11. Prove that nP_(r)=n(n-1)P_(r-1)

Prove that : ^nP_r= n"^(n-1)P_(r-1) , for all natural numbers n and r for which the symbols are defined.

Prove that ^nP_r= ^(n-1)P_r+r^(n-1)P_(r-1) (notation used are in their usual meaning).

Show that ^nP_n= "^nP_(n-1) for all natural numbers n .

Prove that ^(n-1) P_r+r .^(n-1) P_(r-1) = .^nP_r

Prove that .^(n-1)P_r+r.^(n-1)P_(r-1)=^nP_r .

Prove that : ^nP_r= "^(n-1)P_r+r ^(n-1)P_(r-1) , for all natural numbers n and r for which the symbols are defined.

Show that nC_(r)=(n-r+1)/(r)*(nC_(r-1))

Show that , (.^(n)C_(r)+^(n)C_(r-1))/(.^(n)C_(r-1)+^(n)C_(r-2))=(.^(n+1)p_(r))/(r.^(n+1)p_(r-1))

Prove that .^nP_r = ^(n-1)P_r + r^(n-1)P_(r-1)