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

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

Prove :nPr=n(n-1)P(r-1)

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) (notation used are in their usual meaning).

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.

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 .^(n-1)P_(r)+r.^(n-1)P_(r-1)=.^(n)P_(r)